Steelhead trout migrate up stream to spawn. Occasionally they need to leap up small waterfalls to continue their journey. Fortunately, steelhead are remarkable jumpers, capable of leaving the water at a speed of $8.2\,\dfrac{\text{m}}{\text{s}}$. a) What is the maximum height a steelhead trout can jump? b) Leaving the water at $8.2\,\dfrac{\text{m}}{\text{s}}$, the trout lands on the top of the waterfall $2.0\text{ m}$ high. How long was it in the air?

A gyroscope flywheel of radius $2.83 \text{~cm}$ is accelerated from rest at $14.2\text{~ rad/s}^2$ until its angular speed is $2760\text{~ rev/min}$. Through what distance does a point on the rim move during the spin-up?

A gyroscope flywheel of radius $2.83 \text{~cm}$ is accelerated from rest at $14.2\text{~ rad/s}^2$ until its angular speed is $2760\text{~ rev/min}$. What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process?

When the 5 -kg box reaches point A it has a speed $v_{A}=10$ m/s. Determine how high the box reaches up the surface before it comes to a stop. Also, what is the resultant normal force on the surface at this point and the acceleration? Neglect friction and the size of the box.

A speeding motorcyclist is traveling at a constant speed of $36.0 \mathrm{~m} / \mathrm{s}$ when he passes a police car parked on the side of the road. The radar, positioned in the police car's rear window, measures the speed of the motorcycle. At the instant the motorcycle passes the police car, the police officer starts to chase the motorcyclist with a constant acceleration of $4.0 \mathrm{~m} / \mathrm{s}^2$. a) How long will it take the police officer to catch the motorcyclist? b) What is the speed of the police car when it catches up to the motorcycle? c) How far will the police car be from its original position?

John is riding a bicycle at a constant cruising speed along a flat road. He slows down as he climbs a hill. At the top of the hill, he speeds up, back to his constant cruising speed on a flat road. He then accelerates down the hill. He comes to another hill and coasts to a stop as he starts to climb. a) Sketch a possible graph to show John’s speed versus time, and another graph to show his distance travelled versus time. b) Sketch a possible graph of John’s elevation (in relation to his starting point) versus time.

You lean out of your dorm window, which is 12 m above the ground, and toss a 0.12-kg ball up to a friend at a window 11 m above you. (a) What is the slowest initial speed at which you can throw the ball so that he just catches it? (b) If you throw the ball at this speed and your friend misses it, what is its kinetic energy the instant before it hits the ground? (c) Suppose you throw the ball directly downward at the speed calculated in part a. What is its kinetic energy just before it hits the ground?

You (mass 55 kg) are riding a frictionless skateboard (mass 5.0 kg) in a straight line at a speed of 4.5 m/s. A friend standing on a balcony above you drops a 2.5-kg sack of flour straight down into your arms. (a) What is your new speed while you hold the sack? (b) Since the sack was dropped vertically, how can it affect your horizontal motion? Explain. (c) Now you try to rid yourself of the extra weight by throwing the sack straight up. What will be your speed while the sack is in the air? Explain.

What value of magnetic field would make a beam of electrons, traveling to the right at a speed of $4.8 \times 10^6 \mathrm{~m} / \mathrm{s}$, go undeflected through a region where there is a uniform electric field of $8400 \mathrm{~V} / \mathrm{m}$ pointing vertically up?

A block slides up a frictionless, inclined plane with $\theta=25^{\circ}$ (shown in the given figure).

(a) If the block reaches a maximum height $h=4.5 \mathrm{~m}$, what was the initial speed of the block?

(b) Now consider a second inclined plane with the same tilt angle and for which the coefficient of kinetic friction between the block and the plane is $\mu_K=0.15$. What initial speed is now required for the block to reach the same maximum height?

An airplane is heading north at an airspeed of $600 \mathrm{~km} / \mathrm{hr}$, but there is a wind blowing from the southwest at $80 \mathrm{~km} / \mathrm{hr}$. How many degrees off course will the plane end up flying, and what is the plane's speed relative to the ground?

A roller-coaster car at an amusement park has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, assume that its speed is not changing. At the top of the hill, what are the (a) magnitude

$$F_N$$

and (b) direction (up or down) of the normal force on the car from the track if the car’s speed is ν = 11 m/s? What are (c)

$$F_N$$

and (d) the direction if ν = 14 m/s?

A policeman starts giving chase 60 seconds after a stolen car zooms by at 108 km/hr. At what minimum speed should he drive if he has to catch up with the driver before he manages to get onto an expressway 60 km away?

Find each probability.

A coin is tossed $4$ times and it lands heads up, heads up, tails up, and then tails up.