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Chapter 3: Problem 96

A ball is thrown horizontally off the edge of a cliff with an initial speed of \(20.0 \mathrm{m} / \mathrm{s} .\) (a) How long does it take for the ball to fall to the ground 20.0 m below? (b) How long would it take for the ball to reach the ground if it were dropped from rest off the cliff edge? (c) How long would it take the ball to fall to the ground if it were thrown at an initial velocity of \(20.0 \mathrm{m} / \mathrm{s}\) but \(18^{\circ}\) below the horizontal?

Short Answer

Expert verified
Rearranging the equation and solving for \(t\) gives: \(t^2 = \dfrac{2(20)}{9.81}\) \(t^2 ≈ 4.08\) Therefore, \(t = \sqrt{4.08} ≈ 2.02 \mathrm{s}\) In scenario (a) where the ball is thrown horizontally, it takes approximately 2.02 seconds for the ball to hit the ground.

Step by step solution

01

Scenario (a): Ball thrown horizontally

In this scenario, the ball is thrown horizontally off the edge of the cliff with an initial speed of 20.0 m/s. Since the motion of the ball is happening both horizontally and vertically, we'll have separate equations for horizontal and vertical planes. First, we need to find the time it takes for the ball to fall 20.0 m below. Using the vertical motion equation with an initial velocity of 0 (due to no vertical motion initially) and with acceleration due to gravity \(\mathrm{g} = 9.81 \mathrm{m} / \mathrm{s}^2\), we have: \(y = v_{0y} t - 0.5 gt^2\) Plugging in the values, we get: \(20 = 0 - 0.5(9.81)t^2\) Now, we need to solve for \(t\).

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Most popular questions from this chapter

After being assaulted by flying cannonballs, the knights on the castle walls ( \(12 \mathrm{m}\) above the ground) respond by propelling flaming pitch balls at their assailants. One ball lands on the ground at a distance of 50 m from the castle walls. If it was launched at an angle of \(53^{\circ}\) above the horizontal, what was its initial speed?
Geoffrey drives from his home town due east at \(90.0 \mathrm{km} / \mathrm{h}\) for 80.0 min. After visiting a friend for 15.0 min, he drives in a direction \(30.0^{\circ}\) south of west at \(76.0 \mathrm{km} / \mathrm{h}\) for 45.0 min to visit another friend. (a) How far is it to his home from the second town? (b) If it takes him 45.0 min to drive directly home, what is his average velocity on the third leg of the trip? (c) What is his average velocity during the first two legs of his trip? (d) What is his average velocity over the entire trip? (e) What is his average speed during the entire trip if he spent 55.0 min visiting the second friend?
Two displacement vectors each have magnitude \(20 \mathrm{km}\) One is directed \(60^{\circ}\) above the \(+x\) -axis; the other is directed \(60^{\circ}\) below the \(+x\) -axis. What is the vector sum of these two displacements? Use graph paper to find your answer.
A Nile cruise ship takes \(20.8 \mathrm{h}\) to go upstream from Luxor to Aswan, a distance of \(208 \mathrm{km},\) and \(19.2 \mathrm{h}\) to make the return trip downstream. Assuming the ship's speed relative to the water is the same in both cases, calculate the speed of the current in the Nile.
Michaela is planning a trip in Ireland from Killarney to Cork to visit Blarney Castle. (See Example \(3.2 .\) ) She also wants to visit Mallow, which is located \(39 \mathrm{km}\) due east of Killarney and \(22 \mathrm{km}\) due north of Cork. Draw the displacement vectors for the trip when she travels from Killarney to Mallow to Cork. (a) What is the magnitude of her displacement once she reaches Cork? (b) How much additional distance does Michaela travel in going to Cork by way of Mallow instead of going directly from Killarney to Cork?
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