Question

From a tower of height h a particle is projected
horizontally with velocity u and another thrown
down with the same velocity u. If the time taken
by these be t1 and t2what is true ?
A)t1=t2
B)t1>t2
C)t1<t2
D)t1=3t2​

Answer 1

I think it's option (A)...

ignore if it's wrong

Answer 2

Concept:

• Projectile motion
• One-dimensional motion
• Kinematic equations

Given:

• Height of tower = h
• Horizontal velocity in case 1 = u
• Time taken by particle to reach the ground in case 1 = t₁
• Vertical velocity in case 2 = u
• Time taken by particle to reach the ground in case 2 = t₂

Find:

• The relation between t₁ and t₂

Solution:

Consider case 1: Particle is thrown horizontally

The particle has no initial vertical velocity.

We know the following kinematics equation.

s = ut + 1/2 at²

Consider the vertical axis

s = h, u= 0, a = g, t = t₁

h = 0 + 1/2 gt₁²

h = 1/2 gt₁²

t₁² = 2h/g

t₁ = √2h/g

Consider case 2: Particle is thrown down

We know the following kinematics equation.

s = ut + 1/2 at²

s = h, u = u, t = t₂, a = g

h = ut₂ + 1/2gt₂²

t₁ = √2h/g

h = gt₁²/2

gt₁²/2 = ut₂ + gt₂²/2

Based on this equation, we can conclude that t₂ is less than t₁

The correct option is B.

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