Practice Problems 10: Conservation of Energy Begin Date: 10/5/2016 12:00:00 AM D

Question

Practice Problems 10: Conservation of Energy Begin Date: 10/5/2016 12:00:00 AM Due Date: 5/4/2017 12:03:00 AM End Date: 5/4/2017 12:03:00 AM (7%) Problem 5: A football of mass m 1 kg is thrown at an initial velocity of vo 19 m/s at an angle of 6 32 with respect to the horizontal. The ball reaches a maximum height of h. Let gravitational potential energy be zero at ground level h V Otheexpertta.com A 33% Part (a) Give an expression for the initial velocity vector in rectangular form. Write your answer in terms of vo, 0, and the unit vectors i and j Grade Summary Deductions 0% Potential 100%% 7 8 9 cos (o) cos(p) cos (e) Submissions Attempts remaining: 3 sin (o) sin (p) sin(e) 4 5 6 (4% per attempt) 1 2 3 detailed view Submit I give up! Feedback: 5% deduction per feedback. Hints: 4% deduction per hint. Hints remaining: 2 33% Part (b) Write an expression for the potential energy, Ug, of the football at the peak of its trajectory, in terms of the variables given in the problem statement. A 33% Part (c) How high did the ball travel, h, in meters?

Explanation / Answer

mass, m=1kg

inital velocity, vo=19 m/sec

angle, theta=32 degrees

a)

v=vo*cos(theta)i + vo*sin(theta)j

v=19*cos(32)i + 19*sin(32)j

v=(16.11)i + (10.07)j

b)

P.E=m*g*h

c)

time taken to reach the maximum height, t=vo*sin(theta)/g

t=19*sin(32)/9.8

t=1.03 sec

and

h=vo*sin(theta)*t -1/2*g*t^2

h=19*sin(32)*1.03 - 1/2*9.8*1.03^2

h=5.17 m

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