Determine the magnitude and direction of the boats velocity

Question

Assignment:

Question 1:- You throw a ball vertically upward from the roof of a tall building. The ball leaves your hand at a point even with the roof railing with an upward speed of 15.0 m/s; the ball is then in free fall. On its way back down, it just misses the railing. Find

a) the ball's position and velocity 1.00 s, 2.00 s, 3.00 s, and 4.00 s after leaving your hand;

b) the ball's velocity when it is 5.00 m above the railing;

c) the maximum height reached;

d) the ball's acceleration when it is at its maximum height.

e) At what time after being released has the ball fallen 5.00 m below the roof railing? and what will it's speed be at that time?

f) At what time after being released has the ball fallen 2.00 m below the roof railing? and what will it's speed be at that time?

Question 2:- The boat in Figure is heading due north as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the magnitude and direction of the boat's velocity with respect to an observer on the riverbank.

Question 3:- A batter hits a baseball so that it leaves the bat at speed v₀ = 37.0 m/s at an angle α₀ = 53.1°.

a) Find the position of the ball and its velocity (magnitude and direction) at t = 2.00 s.

b) Find the time when the ball reaches the highest point of its flight, and its height h at this time.

c) Find the horizontal range R that is, the horizontal distance from the starting point to where the ball hits the ground. Figure:

Question 4:- Two tanks are engaged in a training exercise on level ground. The first tank fires a paint-filled training round with a muzzle speed of 250 m/s at 10.0° above the horizontal while advancing toward the second tank with a speed of 15.0 m/s relative to the ground. The second tank is retreating at 35.0 m/s relative to the ground, but is hit by the shell. You can ignore air resistance and assume the shell hits at the same height above ground from which it was fired. Find the distance between the tanks

a) when the round was first fired and

b) at the time of impact.

Question 5:- Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown Figure.

a) Find the x and ycomponents of each of the three pulls.

b) Use the components to find the magnitude and direction of the resultant of the three pulls.

Question 6:- Two horses are pulling a barge with mass 2.00*10³ kg along a canal, as shown in Figure. The cable connected to the first horse makes an angle of θ₁ = 30.0° with respect to the direction of the canal, while the cable connected to the second horse makes an angle of θ₁ = 30.0. Find the initial acceleration of the barge, starting at rest, if each horse exerts a force of magnitude 6.00*10² N on the barge. Ignore forces of resistance on the barge.

Question 7:- Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0. If dog A exerts a force of 270 N and dog B exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with dog A's rope.

Question 8:- A 68.5-kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?

Question 9:- You walk into an elevator, step onto a scale, and push the "up" button. You also recall that your normal weight is 625 N. Start answering each of the following questions by drawing a freebody diagram.

a) If the elevator has an acceleration of magnitude 2.50 m/s², what does the scale read?

b) If you start holding a 3.85-kg package by a light vertical string, what will be the tension in this string once the elevator begins  accelerating?

Question 10:- A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude 3.00 m/s2, what is the mass of the box?

Question 11:- Boxes A and B are in contact on a horizontal, frictionless surface, as shown in Figure. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

Question 12:- Two objects of mass m₁ and m₂, with m₂ > m₁, are connected by a light, inextensible cord and hung over a frictionless pulley, as in Active Figure. Both cord and pulley have negligible mass. Find the magnitude of the acceleration of the system and the tension.

Question 13:- A 150-N bird feeder is supported by three cables as shown in Figure. Find the tension in each cable.

Question 14:- An object with mass m₁ = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m₂ = 10.0 kg, as shown in Figure.

a) the acceleration of each object and

b) the tension in the cable.