vertical and horizontal motions of projectiles are independent,?

Question

then why would the range of a mousetrap catapult change the launch angle is changed?

Answer 1

by independent is meant the fact that you can analyse them separately. the horizontal component is affected by both the initial horizontal speed and gravity, whereas the horizontal component is affected only by the initial vertical speed.
if you change the angle at which the catapult is charged, you will change the energy stored in the spring (and therefore the speed of the object - elastic energy into kinetic).
a different angle of launch will affect the relationship between the vertical and horizontal component of the speed (the greater the angle, the greater the vertical component and vice versa).

Answer 2

y(t) = h + U sin(theta) t - one million/2 g t^2 is the vertical place at any time t, U is preliminary velocity, theta is launch attitude, h is the launch elevation, and g is g (what else). x(t) = U cos(theta) t is the horizontal place at any time t. So t = x(t)/U cos(theta) and in y(t) we've: y(t) = h + U sin(theta)/U cos(theta) * x(t) - one million/2 g (x(t)/U cos(theta))^2 = h + x(t) tan(theta) - (g/2)/(U cos(theta))^2 * x(t)^2. ANS. As you will see that, supply U, theta, h, and y(t) (the effect elevation) we are in a position to remedy for x(t) by utilising a quadratic calculator. If we plot y(t) vs x(t) we can locate the curve is a downward dealing with parabola. We see this by the quadratic relationship (you answer) between y(t) and x(t). BTW: the two, vertical and horizontal, are actually not autonomous. As you are able to evidently see y(t) ~ the quadratic in x(t)^2 and the based variable vertical place could be desperate for any given horizontal place, that's the autonomous variable. My factor is this, the vertical place relies upon on the horizontal place; so as that they are actually not autonomous.

Answer 3

Because the initial velocity of the projectile in the vertical and horizontal directions is changed.

Answer 4

The simplest way would be for you to look up vectors in wiki.