1) In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.16 m. The mug slides off the counter and strikes the floor 0.40 m from the base of the counter.
(a) With what velocity did the mug leave the counter? (.823) Correct: Your answer is correct. m/s
(b) What was the direction of the mug's velocity just before it hit the floor? Incorrect: Your answer is incorrect. How does the x component of the velocity of the mug just before it hits the floor compare to its initial velocity?° (below the horizontal)
2) A projectile is fired in such a way that its horizontal range is equal to 11.5 times its maximum height.
What is the angle of projection?
°
b)
time of flight
h = 0.5 g t^2
1.16 = 4.9* t^2
t = 0.487 s
vertical velocity of mug
vy = gt = 9.8* 0.487 = 4.768 m/s
Horizontal velocity, vx = 0.823 m/s
direction of mug velocity
phi = arctan ( vy/vx)
phi = 80.2
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2)
R = u^2 sin 2x / g
H = u^2 (sin x) ^2 / 2g
R = 11.5 H
u^2 sin 2x / g = 11.5 u^2 (sin x) ^2 / 2g
2 sin x cos x / g = 11.5 (sin x) ^2 / (2g)
4 cos x = 11.5 sin x
tan x = 4 / 11.5
x = 19.18
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