Chapter 8: Dynamics II: Motion in a Plane

Space scientists have a large test chamber from which all the air can be evacuated and in which they can create a horizontal uniform electric field. The electric field exerts a constant horizontal force on a charged object. A $15g$charged projectile is launched with a speed of $6.0m/s$ at an angle$35°$ above the horizontal. It lands $2.9m$ in front of the launcher. What is the magnitude of the electric force on the projectile?

A $5000kg$interceptor rocket is launched at an angle of $44.7°$. The thrust of the rocket motor is$140700N$

a. Find an equation $y\left(x\right)$that describes the rocket’s trajectory.

b. What is the shape of the trajectory?

c. At what elevation does the rocket reach the speed of sound, 330 m/s?

A motorcycle daredevil plans to ride up a $2.0-m$-high, $20°$ramp, sail across a $10-m$-wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts up the ramp. He is going $11m/s$at that instant, and the rolling friction of his rubber tires (coefficient $0.02$) is not negligible. Does he survive, or does he become crocodile food? Justify your answer by calculating the distance he travels through the air after leaving the end of the ramp.

A rocket-powered hockey puck has a thrust of $2.0N$ and a total mass of $1.0kg$. It is released from rest on a frictionless table, $4.0m$ from the edge of a $2.0m$ drop. The front of the rocket is pointed directly toward the edge. How far does the puck land from the base of the table?

A $500g$model rocket is resting horizontally at the top edge of a $40-m$-high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of $0.5$m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant $20N$horizontal thrust away from the wall.

a. How far from the base of the wall does the rocket land?

b. Describe the rocket’s trajectory as it travels to the ground

A $2.0kg$projectile with initial velocity $\overrightarrow{v}=8.0\hat{ı}\mathrm{m}/\mathrm{s}$experiences the variable force $\overrightarrow{F}=-2.0t\hat{l}+4.0t^2\hat{ȷ}\mathrm{N}$, where $t$ is in $s$.

a. What is the projectile’s speed at $t=2.0$s?

b. At what instant of time is the projectile moving parallel to the$y-$axis?

A $75kg$ man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is spherical.

A $55kg$ astronaut who weighs $180N$ on a distant planet is pondering whether she can leap over a$3.5$-m-wide chasm without falling in. If she leaps at a $15°$ angle, what initial speed does she need to clear the chasm?

Tarzan swings through the jungle on a massless vine. At the lowest point of his swing, is the tension in the vine greater than, less than, or equal to the gravitational force on Tarzan? Explain.

A concrete highway curve of radius $70m$is banked at a $15°$angle. What is the maximum speed with which a $1500kg$ rubber tired car can take this curve without sliding?