Math  /  Trigonometry

Question1. In the diagram below, a force, FF, is applied to the handle of a lawnmower inclined at angle θ\theta to the ground.
The magnitude of the horizontal component of force FF depends on A) the magnitude of force FF, only B) the measure of angle θ\theta, only C) both the magnitude of force FF and the measure of angle 0 D) neither the magnitude of force FF nor the measure of angle θ\theta \therefore Base your answer to the following question on the information and diagram below. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 3535^{\circ} with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.]
The horizontal component of the ball's initial velocity is approximately A) 3.6 m/s3.6 \mathrm{~m} / \mathrm{s} B) 7.0 m/s7.0 \mathrm{~m} / \mathrm{s} C) 4.9 m/s4.9 \mathrm{~m} / \mathrm{s} D) 13 m/s13 \mathrm{~m} / \mathrm{s} i. Base your answer to the following question on the diagram below which represents a ball being kicked by a foot and rising at an angle of 30.30 .^{\circ} from the horizontal. The ball has an initial velocity of 5.0 meters per second. [Neglect friction.]
As the ball rises, the vertical component of its velocity A) decreases B) increases C) remains the same
4. As the angle between a force and level ground decreases from 616^{1} to 3030^{\circ}, the vertical component of the force A) decreases B) increases C) remains the same
5. A force of 100 . Newtons is applied to an object at an angle of 3C3 C from the horizontal as shown in the diagram below. What is the magnitude of the vertical component of this force? A) 0 N B) 50.0 N C) 86.7 N D) 100.N100 . \mathrm{N}
6. The diagram below shows a child pulling a 50 .-kilogram friend on a sled by applying a 300 --newton force on the sled rope at an angle of 4040^{\circ} with the horizontal.

The vertical component of the 300 .-newton force is approximately A) 510 N B) 230 N C) 190 N D) 32 N
7. The vector diagram below represents the horizontal component, H , and the vertical component, FF, of a 24 -newton force acting at 3535^{\circ} above the horizontal.

What are the magnitudes of the horizontal and vertical components? A) FH=3.5 NF_{H}=3.5 \mathrm{~N} and FV=4.9 NF_{V}=4.9 \mathrm{~N} B) FH=4.9 NF_{H}=4.9 \mathrm{~N} and FV=3.5 NF_{V}=3.5 \mathrm{~N} C) FH=14 NF_{H}=14 \mathrm{~N} and FV=20.NF_{V}=20 . \mathrm{N} D) FH=20.NF_{H}=20 . \mathrm{N} and FV=14 NF_{V}=14 \mathrm{~N} Page I

Studdy Solution
For the seventh question, resolve the 24 N force at 35 35^\circ into components: FH=24cos(35)20N F_H = 24 \cos(35^\circ) \approx 20 \, \text{N} and FV=24sin(35)14N F_V = 24 \sin(35^\circ) \approx 14 \, \text{N} . Therefore, the answer is D.

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