A girl throws a ball vertically upwards at 10m/s from the roof of a building 20m high. How long will it take the ball to reach the ground? What will its speed be when it strikes the ground?
To find the time it will take for the ball to reach the ground, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
- s is the distance traveled (in this case, 20m)
- u is the initial velocity (10m/s)
- t is the time taken
- a is the acceleration (in this case, -9.8m/s^2, as the ball is moving upwards against gravity)
Rearranging the equation, we can solve for time:
20 = 10t + (1/2)(-9.8)t^2
Next, let's solve this quadratic equation to find the time taken.
To find the time it takes for the ball to reach the ground, we can use the equation of motion for free-falling objects. Since the ball is thrown vertically upwards, the initial velocity is positive (+10m/s) and the acceleration due to gravity is negative (-9.8m/s^2). The initial position is 20m (the height of the building).
To calculate the time it takes for the ball to reach the ground, we can use the following equation:
s = ut + (1/2)at^2
Here, s represents the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Rearranging the equation to solve for t, we get:
t = (v - u) / a
Substituting the known values, we have:
u = +10m/s
v = 0m/s (since the final velocity is zero when the ball reaches the ground)
a = -9.8m/s^2
s = -20m (since the displacement is negative for downward motion)
Plugging these values into the equation, we get:
t = (0 - 10) / (-9.8)
Simplifying the calculation:
t = 1.02 seconds (rounded to two decimal places)
So, it will take approximately 1.02 seconds for the ball to reach the ground.
To find the speed of the ball when it strikes the ground, we can use the equation:
v = u + at
Here, v represents the final velocity, u is the initial velocity, t is the time, and a is the acceleration.
Substituting the known values, we have:
u = +10m/s
t = 1.02s
a = -9.8m/s^2
Plugging these values into the equation, we get:
v = 10 + (-9.8)(1.02)
Simplifying the calculation:
v ≈ -9.696 m/s
The negative sign indicates the direction is downward, so the speed of the ball when it strikes the ground is approximately 9.696 m/s.
since the height
h = 10t - 4.9t^2, you want t when h=0.
similarly, v = 10-9.8t