Need them all worked out. Step by step. No shortcuts! A man driving a truck at a

Question

Need them all worked out. Step by step. No shortcuts! A man driving a truck at a constant speed of 15 m/s suddenly applies the brakes, bringing the truck to a stop in 5 seconds. Find: The acceleration The total distance traveled The speed at the end of 1 seconds A shot put is tossed for a distance of 20 m. If the angle of elevation is 45 , find: The velocity of projection The time of flight The maximum height reached An arrow is shot straight up with a initial velocity of 25 m/s. Find: The time to reach the highest point The maximum height reached The velocity at the end to 5 seconds A golf ball of 22 g, moving with a speed of 35 m/s. lands on a pile of soft dirt and becomes embedded a distance of 12 cm into it. Assuming constant deceleration during impact, Find: The acceleration The time interval during impact

Explanation / Answer

1. a)

v = v0 + a t

0 = 15 + a*5

a = -3 m/s^2

b) x = v0 t + 1/2 a t^2 = 15*5 -0.5*3*5^2=
37.5 m

c) v = v0 + a t = 15 -3*1 = 12 m/s

2)

R = V^2/g sin( 2 theta)

20 = v^2/(9.81)*sin( 90 degrees)

v = sqrt(20*9.81)= 14 m/s

b) x = v t

t = x/v = 20/(14*cos(45 degrees))=2.02 s

c) max heigth when vy = 0
vy^2 = v0y^2 + 2 a y

0 = (14*sin(45 degrees))^2 -2*9.81*y

y=4.99 m

3)
a) vy = 0
vy = v0y + a t

0 = 25 - 9.81*t
t=2.55 s
b)
max height when vy = 0
vy^2 = v0y^2 + 2 a y
0 = 25^2 - 2*9.81*y
y=31.9 m

c) v = v0 + a t = 25 - 9.81*5= - 24 m/s

4)

v^2 = v0^2 + 2 a x
0 = 35^2 + 2*a*.12
a=-5104 m/s^2

b) v = v0 + a t

0 = 35 - 5104 t

t = 35/5104=0.00686 s

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