Question

A stone is projected from level ground at $t=0sec$ such that its horizontal and vertical components os initial velocity are $10m/s$ and $20m/s$ respectively. Then the instant of time at which tangential and normal components of acceleration of stone are same is (neglect air resistance and $g=10m/s^2$.)

• A. $1sec$
• B. $4sec$
• C. $\frac{1}{2}sec$
• D. $\frac{3}{2}sec$

Answer 1

The correct option is A $1sec$

Step1: Draw a diagram of given problem.

Step2: Calculate time $\left(t\right)$ using its components.

Given, horizontal components $=10m/s$

Vertical components $=20m/s$

As we know, tangential acceleration
$=a=g\sin \theta$

Normal acceleration $=a_n=g\cos \theta$

$=a_t=a_n$(As mentioned in question)

$g\sin \theta =g\cos \theta$

$\theta ={45}^{\circ }$

$v_y=v_x$

$20-\left(10\right)t=10$

$t=1sec$

Final Answer:(c)