Barron's 2nd Edition DT Q19

Barron's Book

19) A ball is thrown horizontally from a height of 20 meters with a velocity of 30 meters per second. We are asked to find the horizontal distance traveled by the ball. We can do this using the kinematic equations. In order to find the horizontal distance traveled, we first need to find the time it takes to hit the ground. After we find the time, we can easily find the horizontal distance.

Since the initial velocity is in the x-direction, there will be no y-component of the velocity. We are also given that the change in distance will be -20 meters. And finally, since the only force acting on the object is gravity, the acceleration must be g ≈ -10 m/s^2. Now, let’s set up a kinematic equation that includes our given variables and time.

Where d is distance, v is velocity, t is time, and a is acceleration

Now we can plug in our values and solve for the time.

Where y is distance in y-direction, v is velocity, t is time, and a is acceleration

Since we know that the time is 2 seconds, we can find the horizontal distance traveled. We can use the same kinematic equation as above, but this time, our time(t) is 2 seconds, out initial velocity(V[ox]) is 30 meters per second, and our acceleration is 0. Now we can plug these values in to solve for the horizontal distance covered.

Where x is distance in y-direction, v is velocity, t is time, and a is acceleration

Answer: E