Question

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $x=100t-\frac{25}{2}t^2$. the maximum height reached is

• A. 100m
• B. 300m
• C. 200m
• D. 125m

Answer 1

Answer: (D)

125m

Answer 2

The correct answer is option (D): 125m

Given upward displacement in time t second

$x=100t\frac{25}{2}t^2$

Initial velocity = $\frac{dx}{dt}=100-25t=100-25\times0=100\,m/s$

At the maximum height velocity $\frac{dx}{dt}=0$

$100-25t=0\Rightarrow t=4$

Maximum height reached $x=100\times4-\frac{25}{2}\times16=400-200=200m$

Hence the maximum height reached is 200m.

The velocity of the missile, when it reaches the ground, is $(\frac{dx}{dt})_{t=8}=100-25\times 8=-100m/s.$