1 . A ball thrown into the air lands on the same horizontal level, 31.0 m away,

Question

1 . A ball thrown into the air lands on the same horizontal level, 31.0 m away, and 2.10 s later. Find the magnitude of the initial velocity. m/s 2. A cargo plane is flying horizontally at an altitude of 10.1 km with a speed of 890 km/h when a battle tank falls out of the loading ramp. How far horizontally is the tank from where it fell off when it hits the ground assuming that the plane continues to fly with constant velocity? km 3. A girl throws a rock horizontally with a velocity of 10.0 m/s from a bridge. It falls 25.0 m to the water below. How far from the bridge does the rock go?(horizontal distance)(g = 9.8 m/s^2) meters 4. A golf ball is hit with an initial velocity of 50.0 m/s at an angle of 3 1 degrees above the horizontal. If the golf ball lands on the same horizontal level, determine the horizontal distance that the golf ball travels. m 5 . A pitcher throws horizontally a fast ball at 123 km/h toward the home plate , which is 18.2 m away. Neglecting air resistance (not a good idea if you are the batter) , find how far the ball drops because of gravity by the time it reaches the home plate. m 6. While you are traveling in a car on a straight, level interstate highway at 70 km/h, another car passes you in the same direction; its speedometer reads 135km/h. (a) Assuming the direction in which the cars are moving is positive, what is your velocity relative to the other driver?

Explanation / Answer

Let R = the given range and t = time:

1) Vsin = g*t/2 (Assuming g = 9.8, a constant in the y direction)
2) Vcos = R/t (Vx is uniform)

Dividing 1) by 2), tan = gt²/(2R) = 34.906°

1) then gives V = [g*t/2]/sin = 17.98 m/s

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2.

Assume negligible air resistance and a flat Earth for simplicity.

First you need to find how long it will take to hit the ground with this equation:

x = vt + (1/2)at²

where:
x = change in height (10.1 km = 10100 m)
v = initial vertical velocity (0 km/h = 0 m/s)
a = acceleration (9.81 m/s)
t = time
10100 = 0t + (1/2)(9.81)t²
t² = 10100 / (9.81/2)
t² = 2059
t = 45.377s

It takes 45.377 s to fall to the ground, now you just need to find out how far it travels horizontally at that time (moving at the same speed as the plane).

Use the same equation, but this time for horizontal components only:

v = (890km/hr)(1000m / 1km)(1hr / 3600s) = 247.22 m/s
t = 45.377 s
a = 0m/s

x = vt + (1/2)at²
x = (247.22 m/s)(45.377 s) + 0
x = 11218 m
x = 11.218 km

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