Chapter 3: Two-Dimensinal Kinematics

A projectile is launched at ground level with an initial speed of$\mathbf{50}\mathbf{.}\mathbf{0}\mathit{m}\mathbf{/}\mathit{s}$at an angle of$\mathbf{30}\mathbf{.}{\mathbf{0}}^{\mathbf{o}}$above the horizontal. It strikes a target above the ground$\mathbf{3}\mathbf{.}\mathbf{00}$seconds later. What are the x and y distances from where the projectile was launched to where it lands?

A ball is kicked with an initial velocity of \(16\,m/s\) in the horizontal direction and \(12\,m/s\) in the vertical direction. (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c) What maximum height is attained by the ball?

A ball is thrown horizontally from the top of a \(60.0 - m\) building and lands \(100.0\,m\) from the base of the building. Ignore air resistance. (a) How long is the ball in the air? (b) What must have been the initial horizontal component of the velocity? (c) What is the vertical component of the velocity just before the ball hits the ground? (d) What is the velocity (including both the horizontal and vertical components) of the ball just before it hits the ground?

An archer shoots an arrow at a $\mathbf{75}\mathbf{.}\mathbf{0}\mathbf{\text{m}}$distant target; the bull’s-eye of the target is at same height as the release height of the arrow.

(a) At what angle must the arrow be released to hit the bull’s-eye if its initial speed is $\mathbf{35}\mathbf{.}\mathbf{0}\mathbf{\text{m}}\mathbf{/}\mathbf{\text{s}}$? In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems.

(b) There is a large tree halfway between the archer and the target with an overhanging horizontal branch$\mathbf{3}\mathbf{.}\mathbf{50}\mathbf{\text{m}}$ above the release height of the arrow. Will the arrow go over or under the branch?

Give a specific example of a vector, stating its magnitude, units, and direction.

Find the following for path B in Figure:

(a) the total distance traveled, and

(b) the magnitude and direction of the displacement from start to finish.

The various lines represent paths taken by different people walking in a city. All blocks are m on a side.

Verify the ranges for the projectiles in Figure 3.41 (a) for $\mathit{\theta }\mathbf{=}\mathbf{45}\mathbf{°}$and the given initial velocities.

(a) Repeat the problem two problems prior, but for the second leg you walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) north of east (which is equivalent to subtracting \({\rm{B}}\) from \({\rm{A}}\) —that is, to finding \({\rm{R'}} = {\rm{A}} - {\rm{B}}\)).

(b) Repeat the problem two problems prior, but now you first walk \(20.0{\rm{ m}}\) in a direction \(40.0^\circ \) south of west and then \(12.0{\rm{ m}}\) in a direction \(20.0^\circ \) east of south (which is equivalent to subtracting \({\rm{A}}\) from \({\rm{B}}\) —that is, to finding \({\rm{R''}} = {\rm{B}} - {\rm{A}} = - {\rm{R'}}\)). Show that this is the case.

Verify the ranges shown for the projectiles in Figure 3.41 (b) for an initial velocity of $\mathbf{50}\mathbf{}\mathbf{\text{m/s}}$at the given initial angles.

Find the following for path C in Figure

(a) the total distance traveled and

(b) the magnitude and direction of the displacement from start to finish.

In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.

Figure: The various lines represent paths taken by different people walking in a city. All blocks are \(120{\rm{ m}}\) on a side.