The residents of a certain social organization located on the Third street in Bl
ID: 1422637 • Letter: T
Question
The residents of a certain social organization located on the Third street in Bloomington want to take revenge on the leader of a rival organization by bombarding the leader's car with water-filled balloons fired from a slingshot. The residents spot the leader's car 50 meters up from the "target area" on Third street, approaching at a constant 15 m/s. The "target area" is 30 meters directly ( that is, horizontally) in front of the social organization's outer wall, which rises vertically 20 meters from the street. The slingshot is located on the edge of the roof, just on top of the outer wall.
a) How much time must elapse until the car reaches the target area?
b) With what horizontal velocity must the balloon be launched from the slingshot to hit the car? (ignoring air resistance)
c) With what vertical velocity must the balloon be launched? (Again, ignore air resistance)
d) What is the total velocity and angle at which the balloon must be launched?
Explanation / Answer
a) time = distance/speed
t = 50/15 = 3.33 s
b) horizontal distance = 30 m
horizontal velocity
Vx = 30/3.33 =9.00 m/s
c) vertical displacement
y = 20m
y = Vyt +(1/2)gt2
plugging in the values we get
Vy = 10.3 m/s
d) V2 = Vx 2 +Vy2
solving we get
V = 13.67 m/s
if angle is A
tan A = Vy/Vx
=> A = 48.8 degrees to the horzontal