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Is this vector addition or subtraction? Then solve: If you were trying to cross a river with the shortest possible time, would you aim your boat slightly upstream, directly across the river, or slightly downstream?Explain.

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The 2-D Cartesian position vector r for a particle in motion is shown below in meters where t is in seconds: r = 7 t5 - 4 t4 + 8 t3 i + 4 t3 + 5 t4 - 3 t5 j At time = 3 seconds, determine the magnitude of the acceleration vector in m/s/s.
An arrow is launched from ground level, with an initial speed of 27.2 m/s at an angle of 31.4° above the horizontal. Neglect air resistance, and take upward as the positive direction. a) How much time is needed for the arrow to reach its maximum height, b) what is this maximum heightc) how long does it take to land on the ground againd) how far does it travel right before it lands.
Two carts have velocities vand v, respectively. At t = 0 the distance between the two carts were zero. A passenger in cart A wants to throw a ball to cart B. The ball's initial speed with respect to cart A is vo. (a) What angle should the projectile have to reach cart 2? (b) What will be the projectile's speed at maximum height with respect to cart A, cart B, and the ground respectively? A UA B VB
A projectile is fired with initial speed 150 m/s and an angle of elevation 45° from a position 10 m above ground level. Where does the projectile hit the ground and with what speed? Solution If we place the origin at ground level, then the initial position of the projectile is (0, 10) and so we need to adjust the parametric equations of the trajectory by adding 10 to the expression for y. With v0 = 150 m/s, ? = 45°, and g = 9.8 m/s2, we have x = 150 cos ? 4 t = y = 10 + 150 sin ? 4 t − 1 2 (9.8)t2 = . Impact occurs when y = 0, that is 4.9t2 − 75 2 t − 10 = 0. Solving this quadratic equation (and using only the positive value of t), we get the following. (Round your answer to two decimal places.) t = 75 2 + 11,250 + 196 9.8 ≈ Then x ≈ 75 2 (21.74) ≈ (rounded to the nearest whole number), so the projectile hits the ground about…
Is this vector addition or subtraction? Then solve: An airplane flies with a velocity of 55.0m/s [35°N of W] with respect to the air (this is known as air speed). If the velocity of the airplane according to an observer on the ground is 40.0m/s [53°N of W], what was the wind velocity?
An ant undergoes three successive displacements: ?⃗1=3.00 m,20.0 degrees south of east ?⃗2=2.00 m,north ?⃗3=7.00 m,35.0 degrees west of south a) Carefully sketch and label the three displacements with their tails at the origin. Use a coordinate system in which the positive x-axis is east and the positive y-axis is north. b) Calculate the x-and y-components of each of the displacements. c) Use the results of part b) to calculate the distance between where the ant begins and where it ends. d) What fourth displacement (magnitude and direction) is necessary to return the ant to its initial position?
In the homecoming game, the field goal kicker attempts to make a 47 yard (43 m) field goal. He kicks with an initial velocity of 20 m/s at an angle of 60° The field goal posts are 3 m high. Does he make the field goal? Explain your answer. Edit View Insert Format Tools Table 12pt v Paragraph v |BIU
Lesson: Projectiles When there is air resistance present how to the velocity and acceleration vectors behave? O The acceleration vector is perpendicular to the trajectory and the velocity vector is at a tangent to it. O The acceleration changes throughout the flight with its x-component opposite the direction of motion. The velocity vector is at a tangent to the trajectory O The acceleration vector is constant and points straight down. The velocity vector is at a tangent to the trajectory O The acceleration and velocity vectors are both constant magnitude but continually change direction.
A soccer ball is kicked with an initial horizontal velocity of 18 m/s and an initial vertical velocity of 13 m/s. 1) What is the initial speed of the ball? 2) What is the initial angle ? of the ball with respect to the ground? 3) What is the maximum height the ball goes above the ground? 4) How far from where it was kicked will the ball land?