Chapter 2: Q56P (page 36)

Figure 2-35 shows the speed v versus height y of a ball tossed directly upward, along a y axis. Distance d is0.40 m. The speed at height $y_{A}$ is $v_{A}$ .The speed at height $y_{B}$ is $\frac{1}{3} V_{A}$ . What is speed $V_{A}$ ?

Short Answer

Expert verified

The speed of a ball at height $y_{A}$ is $V_{A} = 3.0 m / s$ .

Step by step solution

Given Data

Given,

$V_{B} = \frac{1}{3} V_{A}$

$y_{B} - y_{A} = 0.40 m$

Understanding the concept of motion with constant acceleration

This problem is based on kinematics in which the motion of an object can be

determined with constant acceleration. The speed at a given location can be

found by using a kinematic equation.

Formula

$v_{f}^{2} = v_{i}^{2} + 2 a s (i)$

Calculation of speed

Rewrite the equation (i) using the given data.

$v_{B}^{2} = V_{A}^{2} + 2 (g) (y_{B} - y_{A})$ (ii)

For the vertical motion, $g = - 9.8 m / s^{2}$

Substitute the values in equation (ii).

$v_{B}^{2} = V_{A}^{2} + 2 (- 98) (0.40) \frac{1}{9} V_{A}^{2} = V_{A}^{2} - 7.84 7.84 = V_{A}^{2} - \frac{V_{A}^{2}}{9} 7.84 = \frac{8}{9} V_{A}^{2} 8.82 = V_{A}^{2} V_{A} = 2.969 m / s \approx 3 m / s$

Therefore, the value of $v_{A}$ is 3 m/s .

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Figure 2-35 shows the speed v versus height y of a ball tossed directly upward, along a y axis. Distance d is0.40 m. The speed at height $y_{A}$ is $v_{A}$ .The speed at height $y_{B}$ is $\frac{1}{3} V_{A}$ . What is speed $V_{A}$ ?

Short Answer

Step by step solution

Given Data

Understanding the concept of motion with constant acceleration

Calculation of speed

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Figure 2-35 shows the speed v versus height y of a ball tossed directly upward, along a y axis. Distance d is0.40 m. The speed at heightyAisvA.The speed at heightyBis13VA. What is speedVA?

Short Answer

Step by step solution

Given Data

Understanding the concept of motion with constant acceleration

Calculation of speed

One App. One Place for Learning.

Most popular questions from this chapter

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Figure 2-35 shows the speed v versus height y of a ball tossed directly upward, along a y axis. Distance d is0.40 m. The speed at height $y_{A}$ is $v_{A}$ .The speed at height $y_{B}$ is $\frac{1}{3} V_{A}$ . What is speed $V_{A}$ ?