*Please include formulas + explanations* A) An airplane starts from rest and acc

Question

*Please include formulas + explanations*

A) An airplane starts from rest and accelerates at 10.8 m/s2. What is the speed at the end of a 400m long runway?

B) An object is thrown upwards with a speed of 14 m/s. How high above the projection point is it after .50 sec.?

C) A car is moving with a velocity (3.0 m/s)x + (1.0 m/s)y and 3.0 seconds later its velocity is (6.0m/s)x - (3.0 m/s)y. What is the direction of the average acceleration of the car?

D) A ball rolls over the edge of a table with a horizontal velocity v m/s. The height of the table is 1.6 m and the horizontal range of the ball from the base of the table is 20 m. What is the magnitude and direction of the ball's acceleration right before it touches the ground?

E) A bullet is fired from ground level with a speed of 150 m/s at an angle 30.0° above the horizontal at a location where g = 10.0 m/s2. What is the vertical comonent of its velocity after 4 seconds?

Explanation / Answer

A)
vf^2 = vi^2 + 2ax
vi = 0, a = 10.8, x = 400
vf = sqrt(2ax) = 93.0 m/s

B)
y = y0 + v0t + .5at^2
y0 = 14, v0 = 0, t = 0.50, a = g = -9.8 m/s^2
y = 5.78 m

C)
vx = 6 - 3 = 3 m/s
vy = -3 - 1 = -4 m/s
t = 6
a = v/t
ax = 3/6 = 0.5 m/s^2
ay = -4/6 = -0.67 m/s^2
a = sqrt(ax^2 + ay^2) = 0.833 m/s^2
direction = tan-1(y/x) = -53.1 degrees

D)
The only force on the ball is gravity, which goes straight down. Therefore, the acceleration is the acceleration due to gravity in the downward direction.
a = g = 9.81 m/s^2
direction = down

E)
vy = v*sin(theta) = 150*sin(30) = 75 m/s
a = -10 m/s^2
v = v0 + at = 75 - 10*4 = 35 m/s

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