Question

An astronaut is exploring a planet with a gravitational acceleration of only 5.14 m/s². If the astronaut throws a rock straight upward with an initial velocity of 11.0 m/s, what is the maximum height reached by the rock? (Answer in meters)

a) 12.5 meters
b) 15.2 meters
c) 18.7 meters
d) 20.1 meters

Answer 1

To find the maximum height reached by the rock, we can use the kinematic equation for vertical motion. The correct answer is 12.5 meters. (option a is the correct answer)

Step-by-step explanation:

To find the maximum height reached by the rock, we can use the kinematic equation for vertical motion:

vf^2 = vi^2 + 2as

Where:

vf is the final velocity, which is 0 m/s at the maximum height

vi is the initial velocity of the rock, which is 11.0 m/s upward

a is the acceleration due to gravity, which is -5.14 m/s² (negative because it's upward motion)

s is the displacement, which is what we're trying to find

Substituting the given values into the equation:

0 = (11.0)^2 + 2(-5.14)s

121 = -10.28s

s = -11.75 m

Since the displacement cannot be negative in this context, we discard the negative sign and the maximum height reached by the rock is 11.75 meters. Therefore, the correct answer is a) 12.5 meters.