Please explain and show your work neatly so that I can understand thank you.

30) A curve has a radius of R and a banking angle of 0. Assuming a static coefficient of friction Ms of the car's tires to the road, what is the speed you can safely use for the car to not slide up or down the embankment? R A Draw a FBD of the car on the bank. B Solve for the required speed. C What would happen if the car's speed was lower than your answer from (B)? D What would happen if the car's speed was higher than your answer from (B)? E Assuming there is absolutely no friction between the car's tires and the road - could the car still get around the curve? If so, what is the precise speed required? If not, explain. Hint: How can you change your answer from (B) to model this new sit- uation?32. A block of mass 2 kg is sent sliding onto a frictionless surface at a velocity of 5 m/s. It collides with a stationary block of mass 1 kg. After the collision the 2 kg block is deflected atan angle of 45 degrees with the incoming direction. If the final velocity of the 2 kg block is 2 m/s, find the following: A) Initial momentum of the combined system of the two blocks in X and Y directions. B) Final momentum of the 2 kg block in X and Y directions. C) Final momentum of the 1 kg block in X and Y directions. D) Angle that the 1 kg block makes with the incoming direction after collision. E) Speed of the 1 kg block after collision.42) A block of mass m1=10kg slides on a frictionless surface with a velocity of v1=8m/s and collides with another block of mass m2= 5kg moving at v2=2 m/s. After the collision both blocks continue sliding together in the same direction, i.e., assume a perfectly inelastic collision. a) Draw a sketch of the situation. b) Which quantities are conserved this collision?c) Which quantities are not conserved in this collision in contrast to elastic collisions? d) Calculate the final velocity of both blocks.43) A ball and a cylinder roll down a hill with a total height of h = 2m and total length of s = 10m. Both solids have the same mass m = 2kg, the ball and the cylinder have a radius of r = 10cm. Furthermore, both objects are rolling which means v = wr, where v is the velocity of the centre of mass of the object. S hHint: Jbau = = mr2, Jcyl =; mrz a) Which quantity is conserved in this situation? b) Starting from the conserved quantity in a), calculate the final velocity of the ball. c) How long does it take for the ball to reach the bottom of the hill? d) Would the cylinder be faster or slower? Note: You can give a written argument for d), but it needs to be based on a formula. Alternatively, calculate the time it takes for the cylinder to reach the bottom of the hill