I need help with these physics problems. Someone show me how.?

Question

1-An archer shoots an arrow into a piece of wood. The arrow is traveling at 120 km/h when it strikes the wood. The arrow penetrates 3.8 cm into the wood before stopping. What is its average acceleration in meters per second into the wood?
2-It takes 4.20 s for a ball that was thrown down from the top of a building to reach the sidewalk below. The balls velocity upon striking the sidewalk is 148 mi/h.
a- How tall is the building?
b- What is the initial velocity of the ball?
3-A dragster runs the quarter mile in 8.96 s.
a- What is the cars velocity at the finish line in ft/s and in mi/h?
b- What is the cars average acceleration in ft/s squared?
4- A bullet is fired vertically upward from a gun with an initial velocity of 225 m/s.
a-how high does the bullet go?
b-how long does it take to reach its maximum height?
c-how long is it in flight?

Answer 1

I'll do the first one for you.
u = 120 km/h = 120/3.6 = 100/3 m/s
v = 0
a = ??
s = 3.8 cm = 0.038 m

The formula which relates all these quantities is
v^2 = u^2 + 2as
a = (v^2 - u^2) / (2s)
= -14619.9 m/s^2

Answer 2

Given: Force = 200 N , since, cart is at rest ,initial velocity= 0 , final velocity = 40 m/s , time = 10 s. Find: mass of the cart? Solution: We know that, F=m.a or m=F/a To find the mass m, we need to find acceleration. So, a=v-u/t a=40-0/10 a=4 m/s^2 Now, m=F/a m=200/4 m=50kg.

Answer 3

1. see the above answer

2. Do (b) first

b. 148 mph = 217 ft/sec
...vi = vf - at = 217 - 32 * 4.2 = 82.6 ft/sec

a. x = vi*t + 0.5at^2 = 82.6 * 4.2 + 0.5*32*4.2^2 = 629 ft

3. Do (b) first

b. 1/4 mile = 1320 ft
...a = 2x/t^2 = 2 * 1320/8.96^2 = 32.9 ft/sec^2

a. v = at = 32.9 * 8.96 = 295 ft/sec

4. Do (b) first

b. vf = 0 = vi + at
...t = vi/a = 225/9.8 = 23.0 sec

a. x = vi*t + 0.5at^2 = 225 * 23 - 0.5 * 9.8 * 23^2 = 2580 m

c. 46.0 sec