a child throws a tennis ball vertically upwards at 7.7 m/s from ground level. assuming that no resistance force act on the ball, so that it move only under the influence gravity (9.81 m/s-²), what is the maximum heightin the tennis ball reaches
well,
h(t) = 7.7t - 4.9t^2
max height is reached at t = -b/2a = 7.7/9.8
so plug that in to find h there.
To find the maximum height reached by the tennis ball, we can use the equations of motion.
First, we need to determine the initial velocity and acceleration of the ball. The initial velocity is given as 7.7 m/s and the acceleration is -9.81 m/s² (negative because it is acting against the motion of the ball).
The equation to calculate the maximum height reached is:
\(v_f^2 = v_i^2 + 2 \cdot a \cdot d\)
Where:
- \(v_f\) is the final velocity (which is zero at the maximum height),
- \(v_i\) is the initial velocity,
- \(a\) is the acceleration, and
- \(d\) is the displacement (maximum height).
Rearranging the equation, we get:
\(d = \frac{{v_f^2 - v_i^2}}{{2 \cdot a}}\)
Substituting the given values, we have:
\(d = \frac{{0 - (7.7)^2}}{{2 \cdot -9.81}}\)
\(d = \frac{{-59.29}}{{-19.62}}\)
Simplifying the equation, we find:
\(d = 3.02\) meters
Therefore, the maximum height reached by the tennis ball is approximately 3.02 meters.