Two problems I can\'t seem to get the right answers for. 1. Three people pull si

Question

Two problems I can't seem to get the right answers for.

1. Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 79.1 N, Jill pulls with 60.3 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 141 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey. What is the direction of the net force? Express this as the angle from straight ahead between 0° and 90°, with a positive sign for angles to the left and a negative sign for angles to the right.

2. In deep space, where you can assume that all gravitational and frictional forces are zero, a spaceship fires three different types of objects from three space cannons at exactly the same time so that they leave the spaceship with the exact same speed and in the same direction. They are all headed toward a large target with an initial speed of 67.5 m/s. Assume that the target is 99.5 m away from the space cannons.The properties of the three objects fired are grape= mass of 4.37g tomato= 125g apple=201g. Determine the speed at which each of the objects hits the target.

Explanation / Answer

Jack pulls directly ahead of the donkey with a force of 79.1 N,

Jill pulls with 60.3 N in a direction 45° to the left

Jane pulls in a direction 45° to the right with 141 N.

F(jack)x = 79.1 i
F(jack)y = 0 j

F(jill)x = 60.3*cos45 = 42.63 i
F(jill)y = 60.3*sin45 = 42.63 j

F(jane)x = 141*cos45 = 99.70 i
F(jane)y = 141*cos45 = 99.70 j

Fx = 79.1 i + 42.63 i + 99.70 i = 221.43i N
Fy = 0 + 42.63 j + 99.70 j = 142.33

Fnet = sqrt(Fx^2 + Fy^2)

Fnet = sqrt(221.43^2 + 142.33^2)

Fnet = 236.22 N

Direction can be found out by

Angle = arcTan(y/x)

Angle = arcTan(142.33/221.43)

Angle = 32.61 degrees to the left

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