A tennis ball is thrown vertically upward with an initial velocity of +7.0 m/s.
What will the ball’s velocity be when it returns to its starting point? The acceleration of gravity is 9.81 m/s^2.
Answer in units of m/s
AND How long will the ball take to reach its starting
point?
Answer in units of s
To find the velocity of the ball when it returns to its starting point, we can use the fact that the velocity at any given point during its motion is equal to the initial velocity plus the acceleration multiplied by the time.
1. First, we need to determine the time it takes for the ball to reach its maximum height. Since the ball is thrown vertically upward, it will reach its maximum height when its velocity becomes zero. We can use the equation:
v = u + at
where v is the final velocity (0 m/s), u is the initial velocity (7.0 m/s), a is the acceleration due to gravity (-9.81 m/s^2), and t is the time we are looking for. Rearranging the equation gives us:
t = (v - u) / a
Substituting the given values, we have:
t = (0 - 7.0) / -9.81
Simplifying gives:
t = 0.713 s (rounded to three decimal places)
2. Now that we know the time it takes for the ball to reach its maximum height, we can find the total time for the ball to return to its starting point. Since the ball goes up for half of the total time and comes down for the other half, the total time will be twice the time it takes for the ball to reach its maximum height:
Total time = 2 * t = 2 * 0.713 = 1.426 s (rounded to three decimal places)
Therefore, the ball will take approximately 1.426 seconds to return to its starting point.
To find the velocity of the ball when it returns to its starting point, we can simply use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Substituting the given values, we have:
v = 7.0 + (-9.81) * 1.426
Simplifying gives:
v = -5.931 m/s (rounded to three decimal places)
Therefore, the ball's velocity when it returns to its starting point will be approximately -5.931 m/s. The negative sign indicates that the ball is moving downward.