Two balls A and B of mass 2kg are launched through the air from the same height (3m) and at same speed (4 m/s).
If the ball A is launched straight upwards, and the ball B is launched horizontally, what is the ratio of their final velocities when they hit the ground?
Your answer should complete the statement:"Ball A's final velocity is ____ times Ball B's final velocity."
A 2000kg car accelerates from rest to 36 m/s in 6 seconds. What must the power output of the engine be in order to accomplish this? Express your answer in kilowatts, to three significant figures.
Ball A: V^2 = Vo^2 + 2g*h = 0
4^2 + (-19.6)h = 0
h = 0.82 m.
ho + h = 3 + 0.82 = 3.82 m. above gnd.
V^2 = Vo^2 + 2g*h = 0 + 19.6*3.82 = 74.9
V = 8.7 m/s.
Ball B: h = 0.5g*T^2 = 3
4.9T^2 = 3
T = 0.78 s. to hit gnd.
V = Vo + gT = 0 + 9.8* 0.78 = 7.64 m/s.
Va/Vb = 8.7/7.64 =
To determine the ratio of their final velocities, we need to calculate the final velocities of both balls and compare them.
Let's start with Ball A, which is launched straight upwards. We know that the initial velocity of Ball A is 4 m/s upwards, and it will experience free fall under gravity.
Using the equation of motion:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity
- vi is the initial velocity
- a is the acceleration due to gravity (approximately 9.8 m/s^2)
- d is the displacement (height) covered
Since Ball A is launched straight upwards, its displacement is the height it was launched from, which is 3m. Therefore, we can rewrite the equation as:
vf_A^2 = vi_A^2 + 2ad_A
Substituting the given values:
vf_A^2 = (4 m/s)^2 + 2 * 9.8 m/s^2 * 3 m
vf_A^2 = 16 m^2/s^2 + 58.8 m^2/s^2
vf_A^2 = 74.8 m^2/s^2
Taking the square root of both sides, we get:
vf_A = √(74.8) m/s
vf_A ≈ 8.65 m/s (rounded to two decimal places)
Now, let's move on to Ball B, which is launched horizontally. Since it doesn't have any vertical motion, we can simply calculate its final velocity using the initial velocity.
Therefore, Ball B's final velocity is the same as its initial velocity, which is 4 m/s horizontally.
Now, we can compare the final velocities of balls A and B:
Ball A's final velocity is approximately 8.65 m/s, and Ball B's final velocity is 4 m/s horizontally.
Calculating the ratio:
Ratio = vf_A / vf_B
Ratio = 8.65 m/s / 4 m/s
Ratio ≈ 2.16
Therefore, the statement can be completed as: "Ball A's final velocity is approximately 2.16 times Ball B's final velocity."