Concept explainers
A basketball star covers 2.80 m horizontally in a jump to dunk the ball (Fig. P4.12a). His motion through space can be modeled precisely as that of a particle at his center of mass, which we will define in Chapter 9. His center of mass is at elevation 1.02 m when he leaves the floor. It reaches a maximum height of 1.85 m above the floor and is at elevation 0.900 m when he touches down again. Determine (a) his time of flight (his “hang time”), (b) his horizontal and (c) vertical velocity components at the instant of takeoff, and (d) his takeoff angle. (e) For comparison, determine the hang time of a whitetail deer making a jump (Fig. P4.12b) with center of mass elevations yi = 1.20 m, ymax = 2.50 m, and yf = 0.700 m.
Figure P4.12
(a)
The time of flight of the basketball star.
Answer to Problem 12P
The time of flight of the basketball star is
Explanation of Solution
Section 1:
To determine: The initial velocity of basketball star to go up.
Answer: The initial velocity of basketball star to go up is
Given information:
The horizontal distance covered by the basket ball star is
From the instant the star leaves the floor until just before he lands, the basketball star is a projectile.
The equation to calculate the upward motion of his flight is,
Substitute
Section 2:
To determine: The final velocity of basketball star to go up.
Answer: The initial velocity of basketball star to go up is
Given information:
The horizontal distance covered by the basket ball star is
Substitute
Section 3:
To determine: The time of flight of the basketball star.
Answer: The time of flight of the basketball star is
Given information:
The horizontal distance covered by the basketball star is
The equation to calculate the hang time of basketball star is,
Substitute
Conclusion:
Therefore, the time of flight of the basketball star is
(b)
The horizontal velocity component of the basketball star at take off.
Answer to Problem 12P
The horizontal velocity component of the basketball star at take off is
Explanation of Solution
Given information:
The horizontal distance covered by the basket ball star is
The formula to calculate horizontal velocity component of the basketball star is,
Substitute
Conclusion:
Therefore, the horizontal velocity component of the basketball star at take off is
(c)
The vertical velocity component of the basketball star at takeoff.
Answer to Problem 12P
The vertical velocity component of the basketball star at takeoff is
Explanation of Solution
Given information:
The horizontal distance covered by the basketball star is
From the section 1 of part (a), the vertical component of the velocity of the basketball star at takeoff is,
Conclusion:
Therefore, the vertical velocity of the basketball star at takeoff is
(d)
The takeoff angle.
Answer to Problem 12P
The takeoff angle is
Explanation of Solution
Given information:
The horizontal distance covered by the basket ball star is
The formula to calculate take off angle is,
Substitute
Conclusion:
Therefore, the takeoff angle is
(e)
The time of flight of the deer.
Answer to Problem 12P
The time of flight of the deer is
Explanation of Solution
Section 1:
To determine: The upward velocity of deer going up.
Answer: The upward velocity of deer going up is
Given information:
The horizontal distance covered by the basketball star is
Substitute
Section 2:
To determine: The upward velocity of deer going down.
Answer: The downward velocity of deer going down is
Given information:
The horizontal distance covered by the basketball star is
Substitute
Section 3:
To determine: The time of flight of the deer.
Answer: The time of flight of the deer is
Given information:
The horizontal distance covered by the basketball star is
The equation to calculate the hang time of deer is,
Substitute
Conclusion:
Therefore, the time of flight of deer is
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Chapter 4 Solutions
Physics for Scientists and Engineers with Modern Physics
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