a girl throws a ball vertically upwards at 5m/s from the roof of a building 20m high
how long will it take the ball to reach the ground? and what will its speed be when it strikes the ground
when at the top, vertical velocity is zero
vf=0=vi+gt solve for t, time to top.
How long it will take to get to the ground?
Hf=Hi+vi*t-1/2 g t^2 hi=20, hf=0, solve for t to get time in the air.
T=1.2
To find how long it will take for the ball to reach the ground and its speed when it strikes the ground, we can use the equation of motion for vertical motion:
h = ut + (1/2) * a * t^2
Where:
h = height (in this case, 20m from the roof)
u = initial velocity (in this case, 5m/s upward)
t = time taken
a = acceleration due to gravity (approximately -9.8 m/s^2, negative because it acts downward)
Since the ball is thrown vertically upwards, the acceleration acting on the ball is the acceleration due to gravity acting opposite to its initial velocity.
Let's solve for the time it takes for the ball to reach the ground:
20 = 5t + (1/2) * (-9.8) * t^2
Rearranging the equation:
(1/2) * (-9.8) * t^2 + 5t - 20 = 0
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case,
a = (1/2) * (-9.8) = -4.9
b = 5
c = -20
t = (-5 ± √(5^2 - 4 * (-4.9) * (-20))) / (2 * (-4.9))
Solving the equation, we get two solutions:
t = 2s (ignoring negative value as time cannot be negative in this context)
So, it will take the ball 2 seconds to reach the ground.
Now let's find the speed at which the ball strikes the ground:
v = u + at
v = 5 + (-9.8) * 2
v = 5 - 19.6
v = -14.6
When the ball strikes the ground, its speed will be 14.6 m/s in the downward direction.
Note: The answer for velocity is negative because the ball is moving downward.