A girl throws a ball vertically upward from a building at an initial height of 55.0 m above the ground with an initial speed of 5.00 m/s.
a) What is the velocity of the ball at the highest point in its trajectory?
b) Calculate the velocity of the ball just before it hits the ground.
c) Calculate the total time of flight of the ball.
a. velocity at highest is zero
b. Initial PE + intial KE = final KE
m*9.81*55+1/2 m 5^2= 1/2 m vf^2
vf^2= 25+2*9.81*55 solve for vf
c. time of flight:
hf=hi+vi*t-1/2 9.8 t^2
0=55+5t-4.9 t^2 solve for t by quadratic equation.
a) LOL - ZERO
b)
well doing C first (t at ground where h = 0)
h = Hi + vi t - 4.9 t^2
0 = 55 + 5 t - 4.9 t^2
4.9 t^2 - 5 t - 55 = 0
solve quadratic for t when height is zero
B) we know t at ground from part c above
v = Vi - g t
v = 5 - 9.81 t
To answer these questions, we can use the equations of motion for an object in free fall.
a) To find the velocity of the ball at the highest point in its trajectory, we can use the equation: vf = vi + gt, where vf is the final velocity, vi is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
1. First, calculate the time it takes for the ball to reach the highest point:
Using the equation h = vit + (1/2)gt^2, where h is the height, vi is the initial velocity, g is the acceleration due to gravity, and t is the time taken, substitute the given values:
55.0 m = (5.00 m/s) * t + (1/2)(-9.8 m/s^2)(t^2)
Rearrange the equation to quadratic form:
4.9t^2 - 5t - 55 = 0
Solve for t using the quadratic formula, and note the positive value.
2. Once you have the time at the highest point, substitute it into the equation vf = vi + gt to find the velocity at the highest point.
b) To calculate the velocity of the ball just before it hits the ground, we can again use the equation vf = vi + gt, but this time, we need to find the time it takes for the ball to reach the ground.
1. Substitute the height of the building (55.0 m) into the equation h = vit + (1/2)gt^2 and solve for t. Remember to use the negative value for g since the ball is moving downward.
2. Plug the value of t into the equation vf = vi + gt to get the final velocity just before hitting the ground.
c) To calculate the total time of flight, we need to consider the time it takes for the ball to reach its highest point and then return to the ground.
1. Double the value of the time obtained for the maximum height, as the time taken to reach the highest point will be equal to the time taken to return to the ground.
2. The total time of flight is the sum of the times to reach the highest point and return to the ground.
By following these steps and using the equations of motion for an object in free fall, you can find the answers to all three questions.