Problem

The gravitational acceleration on Mars is about 3.7 meters per second per second. If a Martian juggler were to throw a ball straight up at a rate of 25 meters per second, how high would the ball go? How long would it take until it came down again? Use the formulas v(t) = v₀ – at for the velocity and d(t) = v₀t – (1/2) at² for the height of the ball.

Solution

We know that when the ball reaches its maximum altitude, its velocity will be zero. So we use the formula

with

Set v(t) equal to zero, then solve for t.

or about 6.76 seconds.

Now that we know the time it takes for the ball to go up, we can find the altitude. Use the formula

Finally, since the ball went up for approximately 6.76 seconds, it will take the same time to come down, for a total of

This is confirmed by finding the altitude of the ball at this time, which should equal zero.