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Q.

Is it true that the vertical distance travelled by a projectile in time $t$ , thrown parallel to the ground, does not depend on its initial speed?

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a

True

b

False

answer is A.

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Detailed Solution

The above statement is true.
Given,
Time taken for the projectile to reach the ground is

t

Acceleration due to gravity

g

We are asked to find the vertical distance travelled by the projectile in

t

seconds. Once it starts its horizontal motion, the velocity turns zero at a certain distance from its horizontal direction. Once the velocity becomes zero, the projectile will start falling under the influence of gravity. So we can consider that the vertical motion of the projectile starts with an initial velocity of zero.
Initial velocity of the projectile

u = 0 m s^{- 1}

Total distance traveled is

S

We know that

S = ut + \frac{1}{2} a t^{2} - - - (a)

a

is the acceleration
Here

a = g

From (a) we can write

S = ut + \frac{1}{2} g t^{2} - - - - (i)

Total vertical distance traveled by the projectile is

h

Substituting all the values in the equation (i), we get

h = 0 \times t + \frac{1}{2} \times g {\times (t)}^{2}

\Rightarrow h = 0 + \frac{g t^{2}}{2}

\Rightarrow h = \frac{1}{2} g t^{2} m

Thus the vertical distance traveled by the projectile in t seconds is

\frac{1}{2} g t^{2} m

Hence we can conclude that the initial speed of the projectile does not affect the vertical distance traveled by it.

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