ENG 102 Winter 2023
Homework 1
Due Friday 01/20/2023 by 11:59 pm, Canvas
1. The elevator of a building runs vertically about 350 m and for most of its run has a constant speed
of 22 km/h. Assume that both acceleration and deceleration have a constant magnitude of 0.25g
(g = 9.81m/s2 is the gravitational acceleration constant). Determine the time duration t of the
constant-speed phase (3pts).
2. The horizontal motion of a plunger with a shaft is subject to the resistance of the attached disk
which moves through the oil bath. If the velocity of the plunger is v0 = 3m/s in position A where
x = 0 and t = 0, and the deceleration is proportional to v, i.e. a = -kv, where k = 0.5 s-1. Find (a)
the velocity when t = 2.5 s, (b) the position x when t = 2.5 s, and (c) the velocity when x = 3m.
(6pts)
3. A roofer tosses a small tool to the ground. What is the minimum magnitude of the horizontal
velocity v0 for the tool to just miss the roof corner B? Also determine the distance d. (4pts)
4. The muzzle velocity of a long-range rifle (or the initial velocity of the projectile) at A is u = 400
m/s. Determine the two angles of elevation θ which will allow the projectile to hit the mountain
target B. (4pts)
5. In a basketball game, the point guard A intends to throw a pass to the shooting guard B, who is
breaking toward the basket at a constant speed of 3.5 m/s. If the shooting guard is to catch the ball
at a height of 2 m at C while in full stride to execute a layup, determine the speed v0 and launch
angle θ with which the point guard should throw the ball. (4pts)
6. As part of a circus performance, a man is attempting to throw a dart into an apple which is
dropped from an overhead platform. Assume the man has a negligible reflex delay before
throwing the dart. If the dart is released with a speed v0 = 14 m/s, at what distance d below the
platform should the man aim if the dart is to strike the apple before it hits the ground? (3pts)