Ch 04: Kinematics in Two Dimensions

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 04: Kinematics in Two Dimensions

Problem 17b

Chapter 4, Problem 17b

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 25 m/s at an angle 30 degrees above the horizontal. For how much more time was the ball in flight?

Verified step by step guidance

Step 1: Understand the problem. The question asks for the additional time the golf ball was in flight on the moon compared to Earth. The key difference is the free-fall acceleration, which is 1/6 of Earth's gravity on the moon. The initial velocity and launch angle are the same for both cases.

Step 2: Write the formula for the total time of flight for projectile motion. The time of flight is given by:

T = \frac{2}{v}

₀yg, where

v

₀y is the vertical component of the initial velocity and

g

is the acceleration due to gravity.

Step 3: Calculate the vertical component of the initial velocity. Use the formula:

v

₀y = v₀sinθ, where

v

₀ is the initial speed (25 m/s) and

θ

is the launch angle (30 degrees).

Step 4: Substitute the values of

g

for Earth and the moon. On Earth,

g = 9.8

m/s², and on the moon,

g = \frac{9.8}{6}

m/s². Use these values to calculate the time of flight for both cases.

Step 5: Find the difference in time of flight. Subtract the time of flight on Earth from the time of flight on the moon:

Δ T = T

_moon - T_earth. This will give the additional time the ball was in flight on the moon.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to gravitational forces. It can be analyzed by breaking it into horizontal and vertical components. The horizontal motion is uniform, while the vertical motion is influenced by gravity, which affects the time of flight and the maximum height reached.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates towards the Earth (or another celestial body) due to gravitational force. On the Moon, this acceleration is approximately 1/6th of that on Earth, which significantly affects the time an object remains in the air when projected. This lower gravity results in a longer flight time for projectiles.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In the context of projectile motion, these equations can be used to calculate the time of flight, maximum height, and range of the projectile, taking into account the initial speed and launch angle.

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