Question

A player kicks a football with an initial speed of $25{\text{ms}}^{-1}$ at an angle of ${45}^{\circ }$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? $(\text{Take}g=10{\text{ms}}^{-2})$

• A. $h_{max}=10\text{m},T=2.5\text{s}$
• B. $h_{max}=15.625\text{m},T=1.77\text{s}$
• C. $h_{max}=15.625\text{m},T=3.54\text{s}$
• D. $h_{max}=3.54\text{m},T=0.125\text{s}$

Answer 1

The correct option is B $h_{max}=15.625\text{m},T=1.77\text{s}$

Given :
$u=25\text{m/s}$
$\theta ={45}^{\circ }$

The maximum height is given by :

$h_{max}=\frac{u^2{\sin }^2\theta }{2g}$

$h_{max}=\frac{{25}^2{\sin }^2{45}^{\circ }}{2\times 10}=15.625\text{m}$

The time taken to reach the maximum height is :

$T=\frac{u\sin \theta }{g}=\frac{25\sin {45}^{\circ }}{10}=1.77\text{s}$

Hence, $\left(B\right)$ is the correct answer.