Exam 4: Motion in Two Dimensions

Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant.A glob of dough flies off each beater.Each glob lands on the top of a tin the same horizontal distance away and at its initial height.However,one lands later than the other.The explanation is that they left the beaters at angles θ₁ and θ₂ such that:

An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m.What is the magnitude of the instantaneous acceleration of the particle during this time?

A stunt pilot performs a circular dive of radius 800 m.At the bottom of the dive (point B in the figure)the pilot has a speed of 200 m/s which at that instant is increasing at a rate of 20 m/s².What acceleration does the pilot have at point B?

A car travels in a due northerly direction at a speed of 55 km/h.The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal.If the rain is falling vertically with respect to the earth,what is the speed of the rain with respect to the earth?

A hunter wishes to cross a river that is 1.5 km wide and flows with a velocity of 5.0 km/h parallel to its banks.The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water.What is the minimum time for crossing?

A motorcycle daredevil wants to ride up a 50.0 m ramp set at a 30.0° incline to the ground.It will launch him in the air and he wants to come down so he just misses the last of a number of 1.00 m diameter barrels.If the speed at the instant when he leaves the ramp is 60.0 m/s,how many barrels can be used?

A rifle is aimed horizontally toward the center of a target 0.10 km away,but the bullet strikes 10 cm below the center.Calculate the velocity of the bullet just as it emerges from the rifle.

A baseball is hit at ground level.The ball is observed to reach its maximum height above ground level 3.0 s after being hit.And 2.5 s after reaching this maximum height,the ball is observed to barely clear a fence that is 97.5 m from where it was hit.How high is the fence?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

A car travels in a flat circle of radius R.At a certain instant the velocity of the car is 24 m/s west,and the acceleration of the car has components of 2.4 m/s² east and 1.8 m/s² south.What is the radius of the circle?

The speed of a particle moving in a circle 2.0 m in radius increases at the constant rate of 4.4 m/s².At an instant when the magnitude of the total acceleration is 6.0 m/s²,what is the speed of the particle?

A tennis player standing 12.6 m from the net hits the ball at 3.00° above the horizontal.To clear the net,the ball must rise at least 0.330 m.If the ball just clears the net at the apex of its trajectory,how fast was the ball moving when it left the racket?

A rock is thrown from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal.The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 s after being thrown.Assume that the ground is level and that the side of the building is vertical.Determine the speed with which the rock was thrown.

A car travels in a flat circle of radius R.At a certain instant the velocity of the car is 24 m/s west,and the total acceleration of the car is 2.5 m/s² 53° north of west.Which of the following is correct?

A satellite is in a circular orbit 600 km above the Earth's surface.The acceleration of gravity is 8.21 m/s² at this altitude.The radius of the Earth is 6400 km.Determine the speed of the satellite,and the time to complete one orbit around the Earth.

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s.What are the magnitude and direction of the displacement for this trip?

Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal;the y axis is vertically upward.

A particle moves along a circular path having a radius of 2.0 m.At an instant when the speed of the particle is equal to 3.0 m/s and changing at the rate of 5.0 m/s²,what is the magnitude of the total acceleration of the particle?

A 0.20-km wide river has a uniform flow speed of 3.0 m/s toward the east.A boat with a speed of 8.0 m/s relative to the water leaves the south bank and heads in such a way that it crosses to a point directly north of its departure point.How long does it take the boat to cross the river?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The magnitude,in meters,of the plane's displacement from the origin is