5. Two model rockets, as shown in Figure 5, are fired simultaneously from a ledge with the heights of h = 100 m with initial velocities of VOA = VOB = 200 m/s, at initial angles of A = 45° and 0B = 75° with respect to the horizontal. Determine: (a) The time when the projectile A will reach the position that forms an angle α = 20° below the horizontal. (b) The velocity of projectile A at this instant. (c) The velocity of projectile B at this instant and its angle with horizontal. (d) The relative velocity of projectile A with respect to B at this instant. (e) Which of the rockets will hit the ground first? B th A α Figure 5: Projectile motion of rockets

Q.1 A cannon ball is fired downwards from a tower of height h = 50 m with an initial velocity of 18 m/s. Determine the velocity at which the ball hits the ground and the time it takes the ball to fall to the ground.

Ql/ A ball of mass 0.25 kg is shot upward at an angle o 50° to the horizontal with an initial velocity of 35 m/sec. what is the maximum height ? Q2/ A conservative force F, = (35 y> + 28y* + 27y? + 18y? +y + 4)N ,acts on a 8 kg body ,as the body moves along y-axis from y= 3 m to y=6 m .Calculate each of the following : a- The work done by this force. b- The change in the potential energy of the particle. c- The change of kinetic energy. d- The final kinetic energy , if its speed at 3m is 7 m/sec.

A hunter observed a bird flying overhead and estimated the His rifle is If he fires at height at 15 m and its speed at 20 m/second. capable of a muzzle velocity of 48 m/sec. the instant the bird is directly overhead, at what angle should he incline his rifle in order to hit it? How many meters from his position will the bird hit the ground assum- ing that the weight of the bullet compared to the weight of the bird is negligible?

A mass, m = 1 Kg and initial velocity u =10m/s moving to the right collides with another mass, m2=1 Kg and initial velocity U2= 10m/s moving to the left as shown in the figure below. Find the velocities (vi and v2) of the two masses after collision assuming a perfectly elastic collision. (Hint: Use both conservation of momentum and conservation of energy). a, =10m/s Uz = -10m/s %3D m2 = IKg M= 0 NOTE U, is along +n, tahen as 10mis Uz is along - n, theefave take it at - 10m/s

2 kg move in the directions shown in Figure. Before the and m, has an initial velocity of 8 4 kg and m2 || 3) The masses m¡ collision, the momentum of m, is equal to the momentum of m,, m/s. After the collision, the half of kinetic energy is lost. Find the velocities of the masses m, and m, after the collision. (sin60=0.86 cos60=0.5) Vif y y 60 60 m,}-> x V zi Vii = 8 m/s m, Before the collision v2f After the collision

Problem 11.112 - Determine direction of initial velocity for given projectile - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A model rocket is launched from point A with an initial velocity vo of 96 m/s. Also, the rocket's descent parachute does not deploy and the rocket lands a distance d=100 m from A. d= 100 m B Determine the maximum height above point A reached by the rocket. (You must provide an answer before moving on to the next part.) The maximum height above point A reached by the rocket is m.

PROBLEM 5 A cannon with a muzzle speed of 1 000 m/s is used to start an avalanche on a mountain slope. The target is 2 000 m from the cannon horizontally and 800 m above the cannon. At what angle, above the horizontal, should the cannon be fired?

A torpedo was fired at a target ship by a submarine. The torpedo monitor of the target ship detects that 10 seconds pass between the moments when the explosion noise emitted by the water and air is heard. The torpedo travels in a linear orbit in the water. The propagation speed of sound in air is known as 340 m/s and the propagation velocity in water is 1430 m/s. Calculate the distance between the target ship and the torpedo accordingly.

2. A block of mass m=3 kg is sliding along a frictionless inclined surface that makes an angle of o = 30°with respect to the horizontal surface. At the lowest points of the inclined surface, a projectile is fired at a speed of v, = 12 m/s that makes an angle 8, = 45° with respect to the horizontal. Our aim of this problem is to find the time when the projectile will hit the block. e = 450 h = ? Ro= 10 m P= 30° x= ? (a) Find the time when the projectile hits the block. (Given, the initial distance between the block and the projectile along the inclined surface at t=0 is R, = 10 m as shown in the figure) Page 1 of 3 (b) Find the height h, where the projectile will hit the block. (c) Now assume that the projectile hits the block at its maximum range R along the inclined surface and the block is not sliding at all. Then find the maximum range along the inclined surface, Rmax = ?