You throw a ball of mass 1 kilogram upward with a velocity of a=25 m/s on Mars, where the force of gravity is g=−3.711 m/s2. Use your calculator to approximate how much longer the ball is in the air on Mars.
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To find out how much longer the ball is in the air on Mars compared to on Earth, we can analyze the motion of the ball using the kinematic equations.
First, we need to find the time it takes for the ball to reach its highest point. We can use the following kinematic equation to find the time of flight:
v = u + at
where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (25 m/s)
a = acceleration due to gravity on Mars (-3.711 m/s^2)
t = time of flight
0 = 25 - 3.711t
Rearranging the equation:
3.711t = 25
t = 25 / 3.711
t ≈ 6.73 seconds
Now, since the ball takes the same amount of time to reach the highest point on both Earth and Mars, we can conclude that the total time of flight on Mars will be twice this time.
Total time of flight on Mars = 2 * 6.73
Total time of flight on Mars ≈ 13.46 seconds
Therefore, the ball is in the air for approximately 13.46 seconds longer on Mars compared to on Earth.
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