Seven kinematics problems with acceleration and free fall

[Stripe15]

I have a big packet of questions due for physics. I did around 5 of them, but these 7 really frustrate me because I don't know how to do them. Any help would be appreciated.

Some forumlas I know off the top of my head.
FORMULAS: d=1/2gt*2 v= g X t avg v= d/t g= v-v0/t
v= v0 + gt displacement= v1 x t + 1/2gt*2
v2-v0*2 = 2g x displacement
*2 = squared

1. A motorboat traveling on a straight course slows down uniformly from 75 km/h to 40 km/h in a distance of 50m. What is the required acceleration

2. A rifle bullet with a muzzle speed of 330 m/s is fired directly into a special dense material that stops the bullet in cm. Assuming the deceleration is constant, what is the magnitude?

3. The speed limit in a school zone is 40 km/h. A driver traveling this speed sees a child run into the road 13m ahead of his car. He applies the brakes and the car decelerates at a uniform rate of 8.0 m/s2. IF the driver's reaction time is .25s will the car stop before hitting the child. (There seems to be two parts, one about reaction time distance and braking distance.)

4 A boy throws a stone straight upward with an initial speed of 15 m/s on the surface of the Earth (acceleration is 9.80 m/s2). What maximum hieght above the starting point will the stone reach before falling back down.

5. A spring-loaded gun shoots a 0.0050-kg bullet vertically upward with an inital velocity of 21 m/s. What is the hieght of the bullet 3.0 s after firing? At what time is the bullet 12m above the muzzle of the gun.

6. The world trade center and the empire state building in New York City have hieghts of 417m, and 381 m, respectively. If objects were dropped from the top of each, what would be the difference in time in their reaching the ground? What would be the time of fall for Chicago's Sears tower, at 443 m?

7. A ball is projected vertically downward at an inital speed of 14 m/s from a hieght of 65m above the ground. How far does the stone travel in 2.0s? What is its velocity just before it hits the ground?

 

[HallsofIvy]

First, these should be in the homework section.

Second, show us what you have tried yourself.

 

[wais]

First of all, I understand how frustrating it can be to have a large packet of physics questions due. Kinematics problems can be especially tricky, so it's great that you have already completed 5 of them.

For question 1, you can use the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. In this case, v = 40 km/h, u = 75 km/h, and s = 50m. You can solve for a using this formula.

For question 2, you can use the formula v^2 = u^2 + 2as again, but this time, u = 330 m/s, v = 0 m/s, and s is given in cm. You will need to convert the units to meters in order to solve for a.

Question 3 involves both reaction time and braking distance. The total distance the car needs to stop is the sum of the distance it travels during the driver's reaction time and the distance it travels while braking. You can use the formula d = v*t + 1/2at^2 for both parts, where d is the distance, v is the initial velocity, t is the time, and a is the acceleration.

For question 4, you can use the formula v^2 = u^2 + 2as again, but this time, v = 0 m/s and u = 15 m/s. The maximum height will be the distance s.

Question 5 can be solved using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. You will also need to use the formula s = ut + 1/2at^2 to find the height at a specific time.

For question 6, you can use the formula t = √(2h/g), where t is the time, h is the height, and g is the acceleration due to gravity. You can find the difference in time by subtracting the two values.

Question 7 can be solved using the formula d = ut + 1/2at^2, where d is the distance, u is the initial velocity, a is the acceleration, and t is the time. The velocity just before it hits