40. In this problem, a canon fires a shell in order to shoot a car S, moving with a uniform rectilinear motion behind a hill of height 100 m. The canon, placed at a horizontal distance of 146 m from the point A at the bottom of the mountain, fires a shell, at t, = 0, with an initial velocity of magnitude V. = 60 m/s making an angle 53° with the horizontal. Neglect air resistance. Given: cos 53° = 0.6; sin 53° 0.8; g=10 m/s. C. Motion of S 00m 53° 11!H Motion of the shell a) Determine the trajectory equation. b) Deduce that the shell does not hit the mountain (it moves above the point C). c) Determine the speed of the shell as it moves above C. d) Determine the time needed by the shell to reach the ground (duration of the whole journey).

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter4: Motion In Two And Three Dimensions
Section: Chapter Questions
Problem 57P: In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of...
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40. In this problem, a canon fires a shell in order to shoot a car S, moving with a uniform rectilinear
motion behind a hill of height 100 m.
The canon, placed at a horizontal distance of 146 m from the point A at the bottom of the mountain, fires
a shell, at t, = 0, with an initial velocity of magnitude V. = 60 m/s making an angle 53° with the
horizontal.
Neglect air resistance. Given: cos 53° = 0.6; sin 53° = 0.8 ; g=10 m/s.
C.
Motion of S
100m
11!H
Motion of the shell
a) Determine the trajectory equation.
b) Deduce that the shell does not hit the mountain (it moves above the point C).
c) Determine the speed of the shell as it moves above C.
d) Determine the time needed by the shell to reach the ground (duration of the whole journey).
Motion of the car
At to = 0, the car S, considered as a point object, is at B (OB = 160 m), moving at a constant speed of
108 km/h, under the action of the tractive force of the engine of constant magnitude F.
The force of friction along the road is supposed to be constant of magnitude 1500 N.
e) Determine the magnitude of the tractive force exerted by the engine of the car.
1i. Show that the shell will not shoot the car.
ii. Determine the speed that the car must be moving at; in order to be hit by the shell.
Transcribed Image Text:40. In this problem, a canon fires a shell in order to shoot a car S, moving with a uniform rectilinear motion behind a hill of height 100 m. The canon, placed at a horizontal distance of 146 m from the point A at the bottom of the mountain, fires a shell, at t, = 0, with an initial velocity of magnitude V. = 60 m/s making an angle 53° with the horizontal. Neglect air resistance. Given: cos 53° = 0.6; sin 53° = 0.8 ; g=10 m/s. C. Motion of S 100m 11!H Motion of the shell a) Determine the trajectory equation. b) Deduce that the shell does not hit the mountain (it moves above the point C). c) Determine the speed of the shell as it moves above C. d) Determine the time needed by the shell to reach the ground (duration of the whole journey). Motion of the car At to = 0, the car S, considered as a point object, is at B (OB = 160 m), moving at a constant speed of 108 km/h, under the action of the tractive force of the engine of constant magnitude F. The force of friction along the road is supposed to be constant of magnitude 1500 N. e) Determine the magnitude of the tractive force exerted by the engine of the car. 1i. Show that the shell will not shoot the car. ii. Determine the speed that the car must be moving at; in order to be hit by the shell.
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