A stone is thrown horizontally from a cliff 30m high with an initial speed of 20m/s. How far from the cliff does the stone strike the ground?
Answers
Answer:
Height of cliff = 30m
Initial speed = 20m/s
We have to find range of stone
★ First of all we need to find time of flight.
In such kind of height to ground projectile motion, Horizontal component of initial velocity determines range of projectile and vertical component of initial velocity determines time of flight.
Horizontal component of velocity remains constant throughout the motion as no acceleration acts along horizontal direction.
Vertical component of velocity changes with time as acceleration due to acts in downward direction.
➝ t = √2h/g
➝ t = √2(30)/10
➝ t = √60/10
➝ t = √6
➝ t = 2.45 s
★ Calculation of horizontal range :
➝ R = u × t
- u denotes initial velocity
- t denotes time of flight
- R denotes range
➝ R = 20 × 2.45
➝ R = 49 m
Distance of the cliff before it strike the ground = 121.2 m
Given: initial speed = 20 m/s
height of cliff = 30 m
To find : distance of the cliff before it strike the ground = ?
Solution :
we take vertical component of motion and assume initial velocity is zero
Taking the vertical component of motion we can assume that the initial velocity is zero so:
s = 1/ 2 g t²
∴ t =
t =
t = 4.04 s
The horizontal component of velocity is constant so:
Distance = speed x time
d = 30 × 4.04 = 121.2 m
Therefore , Distance of the cliff before it strike the ground = 121.2 m