A body is projected horizontally from the top of a tall tower with a velocity of 30 ms -1. At time t1, its horizontal and vertical components of the velocity are equal and at time t2, its horizontal and vertical displacements are equal. Then t2-t1 is (take, . g=10 ms -2)

Question

A body is projected horizontally from the top of a tall tower with a velocity of 30 ms -1. At time t1, its horizontal and vertical components of the velocity are equal and at time t2, its horizontal and vertical displacements are equal. Then t2-t1 is (take, . g=10 ms -2) (A) 1 s (B) 1.5 s (C) 2 s (D) 3 s

Tardigrade Admin · Accepted Answer

As per first condition, 30=10 t1 t1=3 s As per second condition, 30 t2=(1/2) × 10 t22=t2=6 s ∴ t2-t1=3 s

Q. A body is projected horizontally from the top of a tall tower with a velocity of 30ms−1. At time t1​, its horizontal and vertical components of the velocity are equal and at time t2​, its horizontal and vertical displacements are equal. Then t2​−t1​ is (take, g=10ms−2)

1 s

1.5 s

2 s

3 s

As per first condition, 30=10t1​ t1​=3s As per second condition, 30t2​=21​×10t22​=t2​=6s ∴t2​−t1​=3s

As per first condition,
$30 = 10 t_{1}$
$t_{1} = 3 s$
As per second condition,
$30 t_{2} = \frac{1}{2} \times 10 t_{2}^{2} = t_{2} = 6 s$
$∴ t_{2} - t_{1} = 3 s$