Question

5 formula 1 point a ball is thrown upwards with an initial velocity of 13 m/s. how long does it take the ball to reach its maximum height? answer 6 formula 1 point a football player kicks a ball straight upwards with an initial velocity of 9.9 m/s. calculate the maximum height of the ball. answer

Explanation:

Step1: Identify the relevant kinematic - equation for vertical motion

The equation for the final velocity $v = v_0−gt$ is used. At the maximum - height, the final velocity $v = 0$. The acceleration due to gravity $g = 9.8\ m/s^2$ and the initial velocity $v_0$ is given.

Step2: Solve for time $t$

We have $0 = v_0−gt$. Rearranging for $t$ gives $t=\frac{v_0}{g}$.
For the first question, $v_0 = 13\ m/s$, so $t=\frac{13}{9.8}\approx1.33\ s$.

Step3: For the second question, use the kinematic equation $v^{2}=v_{0}^{2}-2gh$

At the maximum - height $v = 0$. Rearranging the equation $0 = v_{0}^{2}-2gh$ for $h$ gives $h=\frac{v_{0}^{2}}{2g}$.
Given $v_0 = 9.9\ m/s$ and $g = 9.8\ m/s^2$, then $h=\frac{9.9^{2}}{2\times9.8}=\frac{98.01}{19.6}\approx5.0\ m$.

Answer:

1. $1.33\ s$
2. $5.0\ m$