College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 4, Problem 26P

(a)

To determine

The distance covered by the ball when they hit directly upward, and the time to which the ball stays in the air.

(a)

Expert Solution
Check Mark

Answer to Problem 26P

The distance covered by the ball when they hit directly upward is 100m_, and the time to which the ball stays in the air is 9.2s_.

Explanation of Solution

Write the expression for time of projectile to which it reaches the maximum height.

    ttop=v0sinθg        (I)

Here, v0 is the initial velocity, g is the acceleration due to gravity, and θ is the angle of projection.

Write the expression for maximum vertical distance covered by the ball from the ground level.

    ytop=h+v0(sinθ)t12gt2        (II)

Here, h is the initial height.

Use equation (I) in (II).

    ytop=h+v0(sinθ)v0sinθg12g(v0sinθg)2=h+v02sin2θg12(v0sinθ)2g        (III)

Write the expression for end of trajectory.

    ylands=0=h+v0(sinθ)tlands12gtlands2        (IV)

Here, tlands is the time to which the ball stays in the air.

Solve the equation (IV).

    tlands=(v0sinθ)±(v0sinθ)24(12)ghg        (V)

Conclusion:

Substitute, 90° for θ, 1m for h, 45m/s for v0, and 9.8m/s2 for g in the equation (III), to get ytop.

    ytop=1m+(45m/s)2sin290°9.8m/s212(45m/s×sin90°)29.8m/s2=100m

Substitute, 90° for θ, 1m for h, 45m/s for v0, and 9.8m/s2 for g in the equation (V), to get tlands.

    tlands=(45m/s×sin90°)±(45m/s×sin90°)24(12)(9.8m/s2)(1m)9.8m/s2=9.2s

Therefore, the distance covered by the ball when they hit directly upward is 100m_, and the time to which the ball stays in the air is 9.2s_.

(b)

To determine

The distance covered by the ball when they hit at an angle of 70° with respect to the horizontal, and the time to which the ball stays in the air.

(b)

Expert Solution
Check Mark

Answer to Problem 26P

The distance covered by the ball when they hit at an angle of 70° with respect to the horizontal is 92m_, and the time to which the ball stays in the air is 8.7s_.

Explanation of Solution

Conclusion:

Substitute, 70° for θ, 1m for h, 45m/s for v0, and 9.8m/s2 for g in the equation (III), to get ytop.

    ytop=1m+(45m/s)2sin270°9.8m/s212(45m/s×sin70°)29.8m/s2=92m

Substitute, 70° for θ, 1m for h, 45m/s for v0, and 9.8m/s2 for g in the equation (V), to get tlands.

    tlands=(45m/s×sin70°)±(45m/s×sin70°)24(12)(9.8m/s2)(1m)9.8m/s2=8.7s

Therefore, the distance covered by the ball when they hit at an angle of 70° with respect to the horizontal is 92m_, and the time to which the ball stays in the air is 8.7s_.

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