Question

Mr. Richard's science class is conducting a variety of experiments with projectiles and falling objects. Two groups of students are using a slingshot to launch tennis balls from ground level, and two groups are dropping tennis balls from the fire escape.
Below are descriptions of the parameters with which each group launches or drops their tennis balls.

Group A launches a tennis ball straight up with an initial velocity of 19 meters per second.
Group B launches a tennis ball straight up with an initial velocity of 50 feet per second.
Group C drops a tennis ball from a height of 19 meters.
Group D drops a tennis ball from a height of 50 feet.

Determine which group's activities can be modeled by the following equations, where h is the current altitude of the tennis ball.

1. h = -4.9t^2 + 19. (A-B-C-D)
2. h = -16t^2 + 50t. (A-B-C-D)
3. h = -16t^2 + 50. (A-B-C-D)
4. h = -4.9t^2 + 19t. (A-B-C-D)

Answer 1

Answer:

1.  Group C; 2.  Group B; 3.  Group D; 4.  Group A

Step-by-step explanation:

These equations are in the form

$y=-4.9t^2+v_0t+h_0\\\text{or}\\y=-16t^2+v_0t+h_0$, where v₀ is the initial velocity and h₀ is the initial height.

The first equation has no value for v₀ and a value of 19 for h₀.  This means there is no velocity, so the ball is dropped, and since the initial height is 19, it is dropped from 19 meters.  This makes it group C.

The second equation has a value of 50 for v₀ and no value for h₀.  This means the initial velocity is 50 and there is no initial height.  This makes it group B.

The third equation has no value for v₀ and a value of 50 for h₀.  This means there is no initial velocity, so the ball is being dropped, and the initial height is 50.  This makes it group D.

The fourth equation has a value of 19 for v₀ and no value for h₀.  This means the initial velocity is 19 and there is no initial height.  This makes it group A.

Answer 2

KINEMATIC EQUATIONS a = g vf = g * t + vo rf = (1/2) * g * t ^ 2 + vo * t + ro g = gravity t = time Vf =  final speed Vo = initial speed GroupA: h(t) = - 4.9 * t ^ 2 + 19 * t
 Group B: h(t) = - 16 * t ^ 2 + 50 * t
 Group C: h(t) = - 4.9 * t ^ 2 +19