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Abel challenges Kato to use the equation for the time for any projectile to reach maximum height in the absence of air resistance, given by ty,max v, sin 0, and the kinematic equation Y; = Y; + v{sin 0)t -gt, to determine the maximum height, h, of the tennis ball, given the initial launch angle and speed. Which of Kato's attempts is correct? O Kato tries substituting tymax for t, 0 for y, and h for y, and gets h = "f sin? 0, 2g O Kato says that it is not at all possible to determine the maximum height of a tennis ball using these equations. O Kato tries substituting 2t, max for t, 0 O for y, and h for Yp and gets h =. v? sin? 0, v? sin? e, Kato tries substituting tymax for t, 0 for Yµ and h for y, and gets h =

Abel challenges Kato to use the equation for the time for any projectile to reach maximum height in the absence of air resistance, given by ty,max v, sin 0, and the kinematic equation Y; = Y; + v{sin 0)t -gt, to determine the maximum height, h, of the tennis ball, given the initial launch angle and speed. Which of Kato's attempts is correct? O Kato tries substituting tymax for t, 0 for y, and h for y, and gets h = "f sin? 0, 2g O Kato says that it is not at all possible to determine the maximum height of a tennis ball using these equations. O Kato tries substituting 2t, max for t, 0 O for y, and h for Yp and gets h =. v? sin? 0, v? sin? e, Kato tries substituting tymax for t, 0 for Yµ and h for y, and gets h =

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Prelecture Exploration: Position and Time in Projectile Motion Kato and Abel are tennis partners, and are also in the same physics class. They are playing around with the tennis ball machine, which launches tennis balls at an initial speed of 30 m/s. Kato wonders how high and how far the tennis ball can go, and the pair decide to perform several experiments to find out. This simulation shows a projectile launched from the origin. The initial speed of the projectile is 30 m/s. Kato and Abel can use the slider to set the launch angle or enter an angle value by clicking inside the degrees box and then clicking "fire" to set the projectile in motion. They can move the mouse pointer to see readouts of the x- and y-coordinates for any point on the curve. They can click "pause" to stop the simulation at any point and "clear" to remove traces of the projectile paths. Note that in this simulation, air resistance is ignored. y (m) 75 zy =30 m/s 50 25 x (m) 25 50 75 100 125 Launch Angle 50 degrees 90 75 60 15 Time = 0.00 s fire pause clear Click here to open the simulation in a new window. Part 1 of 9 - Maximum Height Kato runs the pitching machine for several different angles, and she and Abel watch carefully to see what angle results in the greatest height. What angle do they find? |90° 45° 15° 30°
Transcribed Image Text:Prelecture Exploration: Position and Time in Projectile Motion Kato and Abel are tennis partners, and are also in the same physics class. They are playing around with the tennis ball machine, which launches tennis balls at an initial speed of 30 m/s. Kato wonders how high and how far the tennis ball can go, and the pair decide to perform several experiments to find out. This simulation shows a projectile launched from the origin. The initial speed of the projectile is 30 m/s. Kato and Abel can use the slider to set the launch angle or enter an angle value by clicking inside the degrees box and then clicking "fire" to set the projectile in motion. They can move the mouse pointer to see readouts of the x- and y-coordinates for any point on the curve. They can click "pause" to stop the simulation at any point and "clear" to remove traces of the projectile paths. Note that in this simulation, air resistance is ignored. y (m) 75 zy =30 m/s 50 25 x (m) 25 50 75 100 125 Launch Angle 50 degrees 90 75 60 15 Time = 0.00 s fire pause clear Click here to open the simulation in a new window. Part 1 of 9 - Maximum Height Kato runs the pitching machine for several different angles, and she and Abel watch carefully to see what angle results in the greatest height. What angle do they find? |90° 45° 15° 30°
30° They are correct. When the launch angle is 90°, the projectile reaches its greatest height. Part 2 of 9 - Maximum Height The friends find that a 90° launch angle produces the greatest tennis ball height for a given launch speed. Kato asks Abel why this is so. Which of Abel's responses is correct? "The horizontal component of velocity determines the greatest height, and when the launch angle is 90°, the horizontal component is maximum. That is why it is 90°." "When the launch angle is 90°, no component of the velocity is moving against the gravitational acceleration; therefore, the height is greatest here." ] "For this 90° angle, the horizontal component of velocity is zero, so the initial velocity is completely in the vertical direction, resulting in greatest height." "For this angle, the vertical component of velocity is zero, so the initial velocity is purely in the horizontal direction." Abel is correct. As Abel recognized, the initial velocity is entirely in the vertical direction for a 90° launch, so the height of the tennis ball is greatest for a launch angle of 90°. Part 3 of 9 - Maximum Height Abel challenges Kato to use the equation for the time for any projectile to reach maximum height in the absence of air resistance, given by tmax - V, sin 0,, and the kinematic equation Y; = Y; + v,(sin 0)t –gt?, to determine the maximum height, h, of the tennis ball, given the initial launch angle and speed. Which of Kato's attempts is correct? v? sin? 0, O Kato tries substituting tymax for t, 0 for y, and h for y, and gets h = 29 O Kato says that it is not at all possible to determine the maximum height of a tennis ball using these equations. Kato tries substituting 2t, max for t, 0 for y, and h for yp and gets h = v? sin? 0, v? sin? 0,. O Kato tries substituting t ma for t, 0 for y, and h for and gets h = Y,max
Transcribed Image Text:30° They are correct. When the launch angle is 90°, the projectile reaches its greatest height. Part 2 of 9 - Maximum Height The friends find that a 90° launch angle produces the greatest tennis ball height for a given launch speed. Kato asks Abel why this is so. Which of Abel's responses is correct? "The horizontal component of velocity determines the greatest height, and when the launch angle is 90°, the horizontal component is maximum. That is why it is 90°." "When the launch angle is 90°, no component of the velocity is moving against the gravitational acceleration; therefore, the height is greatest here." ] "For this 90° angle, the horizontal component of velocity is zero, so the initial velocity is completely in the vertical direction, resulting in greatest height." "For this angle, the vertical component of velocity is zero, so the initial velocity is purely in the horizontal direction." Abel is correct. As Abel recognized, the initial velocity is entirely in the vertical direction for a 90° launch, so the height of the tennis ball is greatest for a launch angle of 90°. Part 3 of 9 - Maximum Height Abel challenges Kato to use the equation for the time for any projectile to reach maximum height in the absence of air resistance, given by tmax - V, sin 0,, and the kinematic equation Y; = Y; + v,(sin 0)t –gt?, to determine the maximum height, h, of the tennis ball, given the initial launch angle and speed. Which of Kato's attempts is correct? v? sin? 0, O Kato tries substituting tymax for t, 0 for y, and h for y, and gets h = 29 O Kato says that it is not at all possible to determine the maximum height of a tennis ball using these equations. Kato tries substituting 2t, max for t, 0 for y, and h for yp and gets h = v? sin? 0, v? sin? 0,. O Kato tries substituting t ma for t, 0 for y, and h for and gets h = Y,max
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