   Chapter 5, Problem 80AP

Chapter
Section
Textbook Problem

Apollo 14 astronaut Alan Shepard famously took two golf shots on the Moon where it’s been estimated that an expertly hit shot could travel for 70.0 s through the Moon’s reduced gravity, airless environment to a maximum range of 4.00 km (about 2.5 miles). Assuming such an expert shot has a launch angle of 45.0°, determine the golf ball’s (a) kinetic energy as it leaves the club, and (b) maximum altitude in km above the lunar surface. Take the mass of a golf ball to be 0.045 0 kg and the Moon’s gravitational acceleration to be gmoon = 1.63 m/s2.

(a)

To determine
The kinetic energy of the golf ball as it leaves the club.

Explanation

Given Info:

The launch angle is 45.0° .

The mass of the golf ball is 0.045kg .

The gravitational acceleration of the moon is 1.63m/s2 .

The golf ball travels a horizontal distance of 4km in 70.0s .

The x-component of the projectile is,

v0,x=v0cosθ

• θ is the angle that the projectile is launched
• v0 is the velocity that the projectile is launched

On re-arranging,

v0=v0,xcosθ       (I)

Formula to calculate the initial kinetic energy of the ball is,

KE=12mv02       (II)

• m is the mass of ball

On substituting equation (I) in (II),

KE=12m(v0,xcosθ)2

Substitute 0

(b)

To determine
The maximum altitude of the launched ball above the lunar surface.

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