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William Tell must split the apple on top of his son’s head from a distance of 27 m. When William aims directly at the apple, the arrow is horizontal. At what angle should he aim the arrow to hit the apple if the arrow travels at a speed of 35 m/s?

Short Answer

Expert verified

The obtained value of the angle is θ=6.2°.

Step by step solution

01

Step 1. Level horizontal range formula

In this problem, the heights of the arrow at the beginning and end are equal; so the formula of horizontal range can be used to determine the angle. Here, the range and the speed of the arrow are already given.

Given data:

The distance from which the apple is split is d=27m.

The speed of the arrow is v=35m/s.

The formula of level horizontal range can be written as:

R=v2sin2θg

Here, θis the required angle, R is the range whose value is d=27m, and g is the gravitational acceleration.

02

Step 2. Determine the angle at which William should aim the arrow

On plugging the values in the above relation, you get:

27m=35m/s2sin2θ9.81m/s2sin2θ=0.216θ=6.2°

Thus, the required angle is θ=6.2°.

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Most popular questions from this chapter

You are on the street trying to hit a friend in his dorm window with a water balloon. He has a similar idea and is aiming at you with his water balloon. You aim straight at each other and throw at the same instant. Do the water balloons hit each other? Explain why or why not.

A hunter is aiming horizontally at a monkey who is sitting in a tree. The monkey is so terrified when it sees the gun that it falls off the tree. At that very instant, the hunter pulls the trigger. What will happen?

(a) The bullet will miss the monkey because the monkey falls down while the bullet speeds straight forward.

(b) The bullet will hit the monkey because both the monkey and the bullet are falling downward at the same rate due to gravity.

(c) The bullet will miss the monkey because, although both the monkey and the bullet are falling down due to gravity, the monkey is falling faster.

(d) It depends on how far the hunter is from the monkey.

An airplane is heading due south at a speed of 688 km/h. If a wind begins blowing from the southwest at a speed of 90.0 km/h (average), calculate (a) the velocity (magnitude and direction) of the plane relative to the ground and (b) how far from its intended position it will be after 11.0 min if the pilot takes no corrective action. [Hint: First, draw a diagram.]

Revisit Example 3–7, and assume that the boy with the slingshot is below the boy in the tree (Fig. 3–40) and so aims upward, directly at the boy in the tree. Show that again the boy in the tree makes the wrong move by letting go at the moment the water balloon is shot.

FIGURE 3-40Problem 36

During baseball practice, a player hits a very high fly ball and then runs in a straight line and catches it. Which had the greater displacement, the player or the ball? Explain.

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