Question

Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment?

A. four times as far
B. the same distance
C. half as far
D. twice as far
E. by a factor not listed above

Answer 1

the correct answer is A, the object goes 4 times as far

Step-by-step explanation:

This is a projectile launching approach. Where the parameter we are controlling is the initial speed and they ask us how far it goes from the initial one. Let's calculate the range with a speed (vo)

R1 = v₀² sin 2θ / g

Now let's double vo, the new speed is

v = 2 v₀

We calculate the scope

R2 = (2v₀)² sin 2θ / g

R2 = 4 v₀² sin 2θ / g

R2 = 4 R1

Therefore the correct answer is A, the object goes 4 times further