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

37) A football player shoots the ball onto the goal from a distance of 25 m with an angle of 45 degrees from the ground. Assume the player aims straight at the goal and an initial velocity of v=20 m/s. Ignore any air resistance. (a) Draw a sketch of the trajectory including the ball and the goal. (b) Find the equations describing the x and y component of the ball. (c) How long does the ball travel until it reaches the goal? (Hint: Use the x coordinate) (d) Calculate the y component when the ball reaches the goal. Does the player score a goal? A typical goal has a height of 2.44 m. (e) If the ball had an initial velocity of 15 m/s, would the player score a goal?38) A hot-air balloon rises straight up with a velocity of v= 5 m/s relative to earth. Assume a person travelling in a train observes the situation. The train travels with a velocity of v= 30 m/s relative to earth towards east. a) Draw a schematic of the situation from the perspective of an observer at rest and one schematic from the perspective of the traveller in the train. In both schematics indicate the approximate direction of travel of both the balloon and the train. b) What are the velocity vectors of the balloon and the train relative to earth? c) What is the velocity vector of the balloon relative to the train? d) What is the apparent angle of the balloon from the perspective of the person on the train? Hint: Draw the velocity vector of the balloon in a coordinate system.39) A child sits on a sled with a total mass of 100 kg (sled + child) which rests on an inclined frictionless plane with an angle of 30 degrees. a) Draw a free body diagram (leave space for part d). b) Calculate the downhill force pointing parallel to the plane. c) Assuming the slope is 50 m long, how long does it take until the child reaches the bottom of the hill? d) Now, we start pulling the sled and the child up the hill again. We pull at an angle of 60 degrees from the plane. Include the applied force in your free body diagram from a). How much force do we need to apply such that the sled does not move?40) A car is driving on a banked curve. The curve has a radius of R = 300m and the banking angle is 0 = 20 degrees. Assume a constant banking and a constant coefficient of friction M=0.8. a) Draw a free-body diagram of the car of the banked curve.b) Solve for the maximal velocity of the car such that it does not slide up the curve. c) What happens if the car's speed is lower than your answer from b? d) Suppose it rained in the morning and there are still wet patches on the curve, reducing the friction coefficient to =0.2. What happens if the car is still going at the same speed as initially? e) Assuming there is no friction between the car and the road, could the car still get around the curve? If yes, what is the velocity? If no, explain. Hint: Use your formula from b