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

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

Group D: h(t) = - 16 * t ^ 2 +50

Answer 2

The general equation for height is:
h = -0.5gt^2 + (v0)t + h0, where g = -9.8 m/s^2 or -32 ft/s^2, v0 = initial velocity, and h0 = initial height.
1) h = -4.9t^2 + 19: -4.9 means the units are in meters, and 19 means that the initial height was 19 m, which is group C.
2) -16t^2 means the units are in feet, and 50t means that the initial velocity was 50 ft/s upwards. This is group B.
3) -16t^2 again means the units are in feet, and 50 means the initial height was 50 ft. This is group D.
4) -4.9t^2 means the units are in meters, and 19 is the initial height of 19 m. This is for group A.