August 29, 2007 - Department of Physics
TA: Tomoyuki Nakayama Tuesday, January 26th, 2010
PHY 2048: Physic 1, Discussion Section 3695
Quiz 2 (Homework Set #3)
Name: UFID:
Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator. You need to show all of your work for full credit.
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A stone is catapulted at time t = 0, with an initial velocity of magnitude 25.0 m/s and at an angle of 60.0º above the horizontal.
a) What are the horizontal and vertical components of the initial velocity?
A component of a vector along an axis is the projection of the vector onto that axis. Therefore,
v0x = v0cosθ = 25 × cos60º = 12.5 m/s
v0y = v0sinθ = 25 × sin60º = 21.7 m/s
b) What are the horizontal and vertical component of its velocity at t = 3.00 s?
A projectile does not accelerate in the horizontal direction. Thus the x-component of its velocity does not change.
vx = v0x = 12.5 m/s
A projectile accelerates at a constant rate in the vertical direction. Thus, the y-component of its velocity changes linearly with time.
vy = v0y-gt = 21.7 - 9.8 × 3 = -7.70 m/s
c) What are the horizontal and vertical components of its displacement from the catapult site at t = 3.00 s?
The horizontal component of a projectile’s velocity is constant, thus the displacement is given by velocity times time interval.
Δx = v0x t = 12.5 × 3 = 37.5 m
The vertical component of the displacement is given by a quadratic function of time.
Δy = v0yt - (1/2)gt2 = 21.7 × 3 - 0.5 × 9.8 × 32 = 21.0 m
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