Exam 3: Vectors and Motion in Two Dimensions

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is

A shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the shell strike the ground? There is no appreciable air resistance, and g = 9.80 m/s² at the location of the cliff.

A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal. At that instant, what is the speed of the projectile with respect to a stationary observer on the ground?

The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river in which the current flows at 5.0 m/s. (a) At what angle, measured from the upstream direction, should the driver head the boat? (b) How many minutes will it take to cross the river if it is 1.6 km wide at that point?

The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m?

A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football?

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

If a vector $\vec { A }$ has components A_x < 0, and A_y > 0, then the angle that this vector makes with the positive x-axis must be in the range

The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively. (a) What is the magnitude of this vector? (b) What angle does this vector make with the positive +y-axis.

For general projectile motion with no air resistance, the horizontal component of a projectile's velocity

The figure shows four vectors, $\vec { A }$ , $\overrightarrow { \mathbf { B } }$ , $\overrightarrow { \mathrm { C } }$ , and $\vec { D }$ . Vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ both have a magnitude of 7.0 cm, and vectors $\overrightarrow { \mathrm { C } }$ and $\vec { D }$ both have a magnitude of 4.0 cm. Find the magnitude and direction of the sum of these four vectors.

Vector $\vec { A }$ has magnitude 2 units and is directed to the north. Vector $\overrightarrow { \mathbf { B } }$ has magnitude $5 \text { units }$ and is directed to the south. Calculate the magnitude and direction of $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } }$ .

The Moon is 3.84 × 10⁸ m from Earth and takes 27.3 days to complete each orbit. What are the magnitude and direction of the acceleration of the Moon, assuming a circular orbit?

A vector $\vec { A }$ has components A_x = 12.0 m and A_y = 5.00 m. (a) What is the angle that vector $\vec { A }$ makes with the +x-axis? (b) What is the magnitude of vector $\vec { A }$ ?

A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s²?

You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning. What should be the diameter of this wheel?

On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race?

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice.)

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground?