In archery, should the arrow be aimed directly at the target? How should your angle of aim depend on the distance to the target?
The arrow should be aimed a bit higher than the target. The angle of the aim depends upon the distance from the target.
When an object is launched under the influence of gravity, it is said to be undergoing projectile motion. The path followed by the object undergoing projectile motion is parabolic.
When an arrow is fired, the only force acting on it is gravitational pull. The following figure shows that the object is undergoing projectile motion. It follows a curved parabolic path instead of a straight-line path. Thus, the arrow also follows a parabolic path.
An object launched under the influence of gravity follows a parabolic path and not a straight-line path. So, the arrow cannot be aimed directly at the target. It needs to be aimed a bit higher than the bull’s eye to counter the effect of gravity.
As the distance from the target increases, the angle needs to be adjusted accordingly. So, the projectile still covers the required horizontal distance. The angle depends on the horizontal distance and the gravitational effect of the space.
A long jumper leaves the ground at above the horizontal plane and lands 8.0 m away. What is her ‘takeoff’ speed ? (b) Now she is out on a kike and comes to the left bank of the river. There is no bridge, and the right bank is 10.0 m away horizontally and 2.5 m below vertically. If she long jumps from the edge of the left bank at with the speed calculated, (a) how long or short of the opposite bank will she land?
A child, who is 45 m from the bank of a river, is being carried helplessly downstream by the river’s swift current of 1.0 m/s. As the child passes a lifeguard on the river’s bank, the lifeguard starts swimming in a straight line (Fig. 3-46) until she reaches the child at a point downstream. If the lifeguard can swim at a speed of 2.0 m/s relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child?
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