Question

At a skills competition, a target is being lifted into the air by a cable at a constant speed. An archer standing on the ground launches an arrow toward the target. The system of equations below models the height, in feet, of the target and the arrow t seconds after it was fired. Which statement most likely describes the situation modeled by this system?

h=8+2t
h=4+32t-16t^2

1The arrow is fired with an initial upward velocity of 2 ft/s.
2The arrow is fired with an initial upward velocity of 4 ft/s.
3The arrow is fired with an initial upward velocity of 8 ft/s.
4 The arrow is fired with an initial upward velocity of 32 ft/s.

Answer 1

From the kinematic equations, s(t) = s_in + (v_in)(t) – (1/2)(g)(t^2). This means that there is an initial distance of 4, initial velocity of 32 and acceleration (in opposite direction of the motion) of 32. Option 4 shows the correct answer.

Answer 2

By definition, the equation of movement in its generic form is given by:

`h(t) = -(1)/(2)gt^2 + v0t + h0`

Where,

g: acceleration due to gravity

v0: initial speed

h0: initial height

The equation for the arrow is given by:

`h = 4 + 32t-16t ^ 2`

Then, according to the definition, the initial velocity of the arrow is:

`v0 = 32`

Answer:

4 The arrow is fired with an initial upward velocity of 32 ft / s.