Proj Motion EX 2
Helena Dedic
A balloon is drifting horizontally with a speed of 15 m/s. A bolt drops from the balloon at a height of 100 m above the ground. Use the v - t graphs to solve this problem.
a. When will the bolt land on the ground?
b. How far from the drop point will it land? Compute the horizontal distance.
c. What is the bolt's velocity 2 s into the flight?
d. With what velocity will it land?
Solution:
The balloon is drifting horizontally. It means that it has a horizontal velocity of 15 m/s. Therefore the velocity has components (15, 0). The bolt has this velocity when it is dropped. The graphs of versus t and versus t can be drawn as follows:
a. The bolt will land on the ground when it moves down 100m or when its displacement is equal to the area under the curve: - 100 = ½ t( - 10 t). Solving this equation we find t = 4.5 s.
b. The bolt travels horizontally at 15 m/s for 4.5 s. It covers the horizontal distance of 67.5 m.
c. The vertical component of the velocity decreases at a rate of 10 m/s every second. Therefore the vertical component of the velocity will be - 20 m/s at t = 2 s. Consequently, the velocity will be (15 m/s, - 20 m/s).
d. The vertical component of the velocity decreases at a rate of 10 m/s every second. Therefore the vertical component of the velocity will be - 45 m/s at t = 4.5 s. Consequently, the velocity will be (15 m/s, - 45 m/s).