A red ball is thrown directly upwards from the ground with an initial velocity of 35.0 m/s. At the same time, a blue ball is thrown directly upwards from he ground with an initial velocity of 10.0 m/s.
1. How high is the red ball when the blue ball reaches its highest point?
2. How fast is the red ball travelling when the blue ball hits the ground?
1. time to blue max ... v / g
red vel @ blu max ... v - g t
ave red vel ... (2 v - g t) / 2
red hgt ... (ave vel) * t
2. blu ... time up = time down
red vel @ blu impact
... v - g(blu flight time)
To find the height of the red ball when the blue ball reaches its highest point, we need to determine the time it takes for the blue ball to reach its highest point.
1. The time it takes for the blue ball to reach its highest point can be found using the equation:
t = v / g
where:
t = time
v = initial velocity
g = acceleration due to gravity (-9.8 m/s^2)
For the blue ball:
t = 10.0 m/s / 9.8 m/s^2 = 1.02 seconds
Now, we can find the height of the red ball at this time using the equation for vertical motion:
h = v0 * t + (1/2) * g * t^2
where:
h = height
v0 = initial velocity
t = time
g = acceleration due to gravity
For the red ball:
h = 35.0 m/s * 1.02 s + (1/2) * (-9.8 m/s^2) * (1.02 s)^2
= 35.7 m
Therefore, the red ball is at a height of 35.7 meters when the blue ball reaches its highest point.
2. To determine the speed of the red ball when the blue ball hits the ground, we need to find the time it takes for the blue ball to reach the ground.
The time it takes for an object to fall to the ground can be calculated using the equation:
t = sqrt(2h / g)
where:
t = time
h = height
g = acceleration due to gravity (-9.8 m/s^2)
For the blue ball:
t = sqrt(2 * 35.7 m / 9.8 m/s^2)
= 2.00 seconds
Now, we can find the speed of the red ball at this time using the equation for vertical motion:
v = v0 + g * t
where:
v = final velocity
v0 = initial velocity
g = acceleration due to gravity
t = time
For the red ball:
v = 35.0 m/s + (-9.8 m/s^2) * 2.00 s
= 16.4 m/s
Therefore, the red ball is traveling at a speed of 16.4 m/s when the blue ball hits the ground.