Question

A ball is thrown vertically upwards with a speed of 120m/s. It's speed at mid point of its path is about (take g=10m/s^2)?

Answer 1

Given Conditions ⇒

Initial speed of the ball = 120 m/s.

Final Speed of the ball = 0 m/s.

Acceleration =  -g.

Using the formula,

v - u = at

-gt = 0 - 120

gt = 120

t = 12 seconds.

Now, This is the total time. But we want the speed at the mid point.

So Time = 12/2 = 6 seconds.

Using the equation,

v - u = at

∴ v - 120 = -10 × 6

v = 120 - 60

v = 60 m/s.

Hence, the velocity at the midpoint of the path is 60 m/s.

Hope it helps.

Answer 2

Answer

Given,

Initial Speed of ball(u) = 120m/s

Final speed of ball (V) = 0m/s

(Since the ball will stop at some point due to pull of Earth's gravity)

Acceleration due to gravity (g) =10m/s^2

In this case the acceleration due to gravity will be negetive since the body in vertically thrown upwards i.e against gravitational pull of earth.

Now, by using equations of kinematics we get =>

V = u +at

=>V = u + (-g) ×t

=>0 = 120 +(-10) ×(t)

=>-120/-10= t

=>t = 12 second

Hence the total time taken by ball to reach the maximum height is 12 seconds.

But according to the question we need the mid time after the ball is thrown vertically upwards

=>Total time/2

=>12/2

=>6 seconds.

Hence the mid time is 6 seconds.

Now, V=? (speed at midpoint of the total path)

U=120m/s

t= 6 seconds

Acceleration(g) =(-10m/s^2)

(as ball is moving Upward against gravitational pull of earth)

Now, by using equations of kinematics we get=>

V= U +at

=>V= 120 + (-10)×6

=>V = 120 - 60

=>V = 60 m/s.

Hence the speed of ball in its halfway will be 60m/s

Remember

##The 3 equations of kinematics =>

1)v = u +at

2)V^2 - u^2 = 2as

3)s = ut + 1/2(at^2)