A 75.0 g bullet is fired at a muzzle velocity of 476 m/s from a gun with a mass 4.75 kg and a barrel length of 60 cm

How long is the bullet in the barrel?

This may be a bit of a trick question. If "muzzle velocity" means the speed of the bullet relative to the barrel of the gun, then you simply need to divide the length of the barrel by the muzzle velocity. But if "muzzle velocity" means the speed of the bullet relative to the ground, and if it's assumed that the gun is not being held steady but rather recoils in a way that is consistent with conservation of momentum, then you need to take into account the recoil velocity of the gun. Conservation of momentum tells you that



You know the two masses and one velocity, so you can solve for the other velocity (of the gun barrel). Then the total velocity of the bullet relative to the barrel is , and the time spent in the barrel is the length of the barrel divided by v_total..

_______ is a vector of quantity

in s.I system the value of g is

I) the total net force F acting on the surface of a dam of height h and width ω am given by the relation
F= (ρ×g×ωh^2)/2 Show that the relation is dimensionally correct where g is the acceleration of gravity and ρ the density

1. I) the total net force F acting on the surface of a dam of height h and width ω am given by the relation
F= (ρ×g×ωh^2)/2 Show that the relation is dimensionally correct where g is the acceleration of gravity and ρ the density/ 5Marks

ii) A motorist travelling 31m/s passes a stationary motor cycle police officer. 2.5s After the motorist passes, the police officer starts to moves and accelerates in pursuit of the speeding motorist. The motorist has constant acceleration of 3.6m/s2 .
a) How fast will the police officer be travelling when he overtakes the car? /2Marks
b) Suppose that for reasons of safety the policeman does not exceed a maximum speed of 45m/s. How long will it then take him to overtake the car, and how far will he travelled? /3Marks

2. A car is moving 60km/h when the driver sees a signal light 40m a head turn red. The car can slow with acceleration -0.5g (where g=9.80m/s2). What is her stopping distance assuming
a) Zero reaction time? /5Marks
b) A reaction time of 0.20s between when she sees the red light and when she hits the brake? /5Marks

3.I)


A painter who weights 600N stands on a platform, shown here . The platform, paint, brushes, and so weight on 400N. What is the tension in the rope the pointer is holding when the platform is motionless?
What is the tension in the rope the pointer is holding when the platform is motionless? /5Marks

ii) Two masses are connected as shown here,



Friction is negligible. What is the acceleration of each mass? What is the acceleration of each mass? What is the tension in the string?/5 Marks

4. A car of mass m= 749.5kg accelerates from rest in ten first seconds . The total force which acts on it is given by the relation F= F0 – kt where k= 44.48N/s, F0 = 889.6N and t = the time during the motion. According Newton's second law, find the speed of the car after 10seconds and the distance at that time/10Marks

5. a) wheel changes its angular velocity with a constant acceleration while rotating with a constant acceleration while rotating about a fixed axis through its centre.
I) Show that the change in the magnitude of the radial acceleration during any time interval of the point on the wheel is twice the product of the angular acceleration. The angular displacement, and the perpendicular distance of the point from the axis./5Marks
ii) The radial acceleration of a point on the wheel that is 0.25m from the axis changes from 25m/s2 to 85m/s2 as the wheel rotates through 15rad. Calculate the tangential acceleration of this point./4Marks


b) An electric engine is tuned off and its angular velocity decreases uniformly from 900revolution per minute to 400revolution per minute in five seconds.
ii) Find the angular acceleration in revolution per second square(rev/s2) and the number of revolution of the engine in 5second interval./4Marks
iii) The time to stop the engine if the angular acceleration remains constant/2Marks

6. a) Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation gT^2=2R tan⁡α where α is the angle of projection./ 5Marks
b) A rifle bullet is fired with a speed of 280m/s up a plane surface that is inclined at 30° above horizontal. The bullet is fired at an initial angle of elevation of 45°above the horizontal. How far up the plane does it land? /10Marks

Show us your attempt at solving each of these and we'll help where you get stuck.