A ball thrown vertically upwards from ground level hits the ground after 4secs.calculate the maximum height it reached during its journey (g=10m/s
To calculate the maximum height reached by the ball, we can use the formula for vertical motion:
h = u*t + (1/2)*g*t^2
Where:
h = maximum height reached
u = initial upwards velocity
g = acceleration due to gravity
t = time taken to reach the maximum height
Given:
g = 10 m/s^2
t = 4 s
To find the initial upwards velocity (u), we can assume that when the ball hits the ground, its final velocity (v) is zero. Then we can use the equation:
v = u + g*t
Since v = 0 when the ball hits the ground, we have:
0 = u + g*t
u = -g*t
Substituting the value of u into the first equation, we have:
h = (-g*t)*t + (1/2)*g*t^2
Simplifying this equation, we get:
h = -(1/2)*g*t^2 + (1/2)*g*t^2
h = 0
Therefore, the maximum height reached by the ball during its journey is 0 meters.
To calculate the maximum height reached by the ball, we can use the equation of motion for vertical motion:
h = u*t + (1/2)*g*t^2
Where:
h = maximum height
u = initial velocity
t = time of flight
g = acceleration due to gravity
In this case, we know that the ball takes 4 seconds to travel to the ground, so the time of flight is 4 seconds. The acceleration due to gravity is given as 10 m/s^2.
Since the ball is thrown vertically upwards, its final velocity at the maximum height would be zero. This means that the time it takes to reach the maximum height is half of the total time of flight.
So, the time to reach the maximum height is 4 seconds / 2 = 2 seconds.
Using the equation of motion, we can substitute the values and calculate the maximum height:
h = u*t + (1/2)*g*t^2
h = 0*t + (1/2)*10*(2^2)
h = 0 + 20
h = 20 meters
Therefore, the maximum height reached by the ball is 20 meters.
v=0 after 2 seconds, so initially v = 9.8*2 = 19.2 m/s
Now, since height h = 19.2t - 4.9t^2 = 19.2 m