Chapter 10: Q85P (page 293)

A golf ball is launched at an angle of $20 °$ to the horizontal, with a speed of $60 m / s$ and a rotation rate of $90 \frac{rad}{s}$ . Neglecting air drag, determine the number of revolutions the ball makes by the time it reaches maximum height.

Short Answer

Expert verified

The number of revolutions the ball makes when at maximum height is $30$

Step by step solution

Given

Angle of launch is $20 °$
Horizontal speed is $60 m / s$
Rotational rate is $90 \frac{rad}{sec}$

Understanding the concept

Find time to reach the maximum height using the kinematic equation. Using this time, find the angle in radians. The angle is nothing but angular displacement, which can be converted into a number of rotations using the relationship between one rotation and angle traced during one rotation.

Formula:

$v_{f y} = v_{0 y} + at$

$θ - θ_{0} = ω_{0} t$

Calculate the number of revolutions the ball makes by the time it reaches maximum height

Time to reach maximum height is as follows:

$v_{f y} = v_{0 y} + at$

At maximum height, the velocity is zero, so

$0 = 60 sin 20 - 9.8 t \Rightarrow t = 2.094 sec$

Now, the number of revolutions:

$θ - θ_{0} = ω_{0} t \Rightarrow θ - θ_{0} = 90 \times 2.094 \Rightarrow θ - θ_{0} = 188 rad$

$188 \times \frac{1 rev}{2 π} = 29.93 rev$

So, the number of revolutions is $30$ .

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A golf ball is launched at an angle of $20 °$ to the horizontal, with a speed of $60 m / s$ and a rotation rate of $90 \frac{rad}{s}$ . Neglecting air drag, determine the number of revolutions the ball makes by the time it reaches maximum height.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the number of revolutions the ball makes by the time it reaches maximum height

One App. One Place for Learning.

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A golf ball is launched at an angle of 20°to the horizontal, with a speed of 60m/sand a rotation rate of 90rads. Neglecting air drag, determine the number of revolutions the ball makes by the time it reaches maximum height.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the number of revolutions the ball makes by the time it reaches maximum height

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Magnetism and Electromagnetic Induction

Waves Physics

Space Physics

Solid State Physics

Force

Study anywhere. Anytime. Across all devices.

A golf ball is launched at an angle of $20 °$ to the horizontal, with a speed of $60 m / s$ and a rotation rate of $90 \frac{rad}{s}$ . Neglecting air drag, determine the number of revolutions the ball makes by the time it reaches maximum height.