11 A boy throws a ball with speed V m/s at an angle of 45° to the horizontal. a Derive expressions for the horizontal and vertical components of the displacement of the ball from the point of projection. b Hence show that the Cartesian equation of the path of the ball is y = x V2

College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A and b only

11 A boy throws a ball with speed V m/s at an angle of 45° to the horizontal.
a Derive expressions for the horizontal and vertical components of the displacement of the ball from
the point of projection.
b Hence show that the Cartesian equation of the path of the ball is y = x -
8x2
V2
c The boy is now standing on a hill inclined at an angle 0 to the horizontal. He throws the ball at
the same angle of elevation of 45° and at the same speed of V m/s. If he can throw the ball 60
metres measured down the hill, but only 30 metres measured up the hill, use the result in part (b) to
show that
30g cos 0
60g cos 0
1,
tan 0 = 1
|
V2
and hence that 0 = tan¬'.
V2
Transcribed Image Text:11 A boy throws a ball with speed V m/s at an angle of 45° to the horizontal. a Derive expressions for the horizontal and vertical components of the displacement of the ball from the point of projection. b Hence show that the Cartesian equation of the path of the ball is y = x - 8x2 V2 c The boy is now standing on a hill inclined at an angle 0 to the horizontal. He throws the ball at the same angle of elevation of 45° and at the same speed of V m/s. If he can throw the ball 60 metres measured down the hill, but only 30 metres measured up the hill, use the result in part (b) to show that 30g cos 0 60g cos 0 1, tan 0 = 1 | V2 and hence that 0 = tan¬'. V2
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