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Chapter 2: Q82GP (page 22)

You stand at the top of a cliff while your friend stands on the ground below you. You drop a ball from rest and see that she catches it 1.4 s later. Your friend then throws the ball up to you, such that it just comes to rest in your hand. What is the speed with which your friend threw the ball?

Short Answer

Expert verified

The obtained speed of the ball is \(u = 13.734\;{\rm{m/s}}\).

Step by step solution

01

Kinematic relation for determining the speed

In this problem, the upward direction is considered positive, and the origin is taken to be at the level where the ball was thrown.

Given data:

The time at which she catches the ball is\(t = 1.4\;{\rm{s}}\).

The relation from the kinematics equation is given by:

\(v = u + gt\)

Here, v is the speed of the ball whose value is zero because the ball is at rest, u is the required initial speed of the ball, and g is the gravitational acceleration.

02

Calculation of initial speed of the ball

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

\(\begin{aligned}0 = u + \left( { - 9.81\;{\rm{m/}}{{\rm{s}}^2}} \right)\left( {1.4\;{\rm{s}}} \right)\\u = 13.734\;{\rm{m/s}}\end{aligned}\)

Thus, \(u = 13.734\;{\rm{m/s}}\) is the required speed.

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Most popular questions from this chapter

Sketch the v vs t graph for the object whose displacement as a function of time is given by Fig. 2-44.

Figure 2-44 Problems 57,58 and 59

A helicopter is ascending vertically with a speed of 5.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is v0 for the package?]

Digital bits on an audio CD of diameter 12.0 cm are encoded along an outward spiraling path that starts at radius R1= 2.5 cmand finishes at radius R2= 5.8 cm. The distance between the centers of the neighbouring spiral windings is 1.6 μ m = 1.6 × 10-6 m.

(a) Determine the total length of the spiral into a straight path [Hint: Imagine ‘unwinding’ the spiral and the straight path of width 1.6 μ m, and note that the original spiral and the straight path both occupy the same area.]

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