Show all work please A car is traveling with a constant speed along a road that

Question

Show all work please A car is traveling with a constant speed along a road that makes a half of a square (two sides out of four). The average velocity of the car is 50 miles/hour. What is its speed? A shooter aims horizontally at a target at the distance d at the same height as the shooter. The initial speed of the bullet is v. by what vertical distance h the bullet will miss the target? A car travels around a circle with a radius R. At what speed v_max the car begins to skid if the static friction coefficient is mu_s?

Explanation / Answer

(1)
Velocity = 50 miles/hr
Velocity = Total Displacement / Total Time

Speed = Total Distance/ Total time

Let the side of square be x.
Let time taken be t .

Total Displacement = sqrt(x^2+x^2) = x*sqrt(2)
Total Distance = x + x = 2x

So,
50 = x*sqrt(2)/t
x/t = 50/sqrt(2) -------1

Speed = 2x/t
Speed = 2 * 50/sqrt(2)
Speed = 70.7 miles/hour

(2)
Horizontal distance = d
Initial Speed of bullet, = v

So time taken to travel distance, t = Distance/Speed = d/v

Now,
Initial Vertical Speed = 0
Vertical acceleration = g = 9.8 m/s^2

So Height by which target will be missed,
s = u*t + 1/2*a*t^2
h = 0 + 1/2 g * (d/v)^2

h = 1/2*g * (d/v)^2 or 4.9 * (d/v)^2

please post seperate questions in seperate post only !!

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