Physics -> Mechanics -> Motion in Two Dimension 

Mech2D-1:

A projectile was fired at an angle of 65 degrees with respect to the horizontal. It has an initial velocity of 60-km/h. When the

projectile was at the top of its trajectory, an internal explosion causes it to separate into 2 fragments of equal mass. One fragment falls straight down as though it was released from rest. How far from the launch point does the other fragment land?

Mech2D-2:

A hunter directly aims at a target that is on the same level as the hunter,120 m away. The bullet leaves the gun at a speed of 250 m/s. (1) By how much will it miss the target? (2) At what angle should the bullet be fired to hit the target? 

Mech2D-3:

A boy throws a rock up an inclined plane with a velocity u. Assuming that the plane makes an angle α with the horizontal and that the rock is thrown at an angle β with respect to the slope, find the position of the rock as a function of time. You may choose the x-y axes along and normal to the slope respectively. Show that the rock hits the ground after a time, t= 2uβ / g cos α. Find the range of the rock and show that it has a maximum value of u^2/[g(1+sin α)].

Mech2D-4:

A bug moves in the x-y plane. At t = 0, it is at the origin and starts to move with a velocity of 0.01 m/s in the +y direction. Bug’s acceleration is given by: a = (0.5 i + 0.8 j) m/s^2 where i and j are unit vectors along x and y directions respectively. What is the bug’s speed when its x coordinate is 1 m?

Mech2D-5:

A rock with an initial speed of 55 m/s was thrown at an

angle θ with respect to the horizontal. If it lands 215 m

away on a level ground, (a) what are the two possible values

of θ for which this result is achieved, (b) what are the

maximum heights reached for both of these possibilities?

Mech2D-6:

A marble rolls off a table top with a speed of 5m/s. Tabletop is 1.6 m above the floor. Where will the marble hit the floor and what velocity components will it have just before it hits the floor?

Mech2D-7:

A projectile is fired at an angle of 30.0° above the horizontal

with an initial speed of 60 m/s. How long does it take the projectile to reach the highest point in its trajectory?

Mech2D-8:

A crate slides down a ramp that is at a 40° incline. The speed of the crate at the bottom would have been 3 times greater if there was no friction present. What is the coefficient of friction between the crate and the ramp?

Mech2D-9:

A ball is projected with an initial speed of 50 m/s at an

angle of 45° above the horizontal.
a) Find the distance the ball travels horizontally.
b) Find the maximum height of the ball during the flight.

Mech2D-10

According to the information given in the following image, what is the initial angle of inclination of the projectile? What is the direction of the final velocity? Show your work. Image