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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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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