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A dolphin jumps out of the water with an initial velocity of 20 feet per

second (assume its starting height is O feet). Use the vertical motion
model, h = - 16t2 + vt +8, where v is the initial velocity in feet per
second and s is the height in feet, to calculate the amount of time the
dolphin is in the air before it hits the water again. Round your answer
to the nearest tenth if necessary.
Time in air: seconds

User Onezeno
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4.1k points

2 Answers

10 votes

Final answer:

The dolphin spends approximately 1.25 seconds in the air before hitting the water again, which is found by setting the vertical motion model equation h = -16t^2 + 20t + 0 to 0 and solving for t.

Step-by-step explanation:

The question involves the use of the vertical motion model to calculate the time a dolphin spends in the air after jumping out of the water with an initial velocity. The model provided is h = -16t2 + vt + s, where h is the height above the starting point, v is the initial velocity (20 feet per second in this case), t is the time in seconds, and s is the starting height, which is given as 0 feet.

To find the time the dolphin is in the air before it hits the water again, we need to determine when h equals 0 after the initial jump (excluding the starting time). Thus, we solve for t when h is equal to 0:

0 = -16t2 + (20)t + 0

Using the quadratic formula, we determine that the non-zero root of this equation gives the time the dolphin is in the air. After calculation, the root that represents the upward and downward motion of the dolphin is approximately 1.25 seconds.

Thus, the dolphin spends approximately 1.25 seconds in the air before it hits the water again.

User Mohit Maru
by
4.3k points
2 votes

Answer:

1.6 Seconds

Step-by-step explanation:

The equation would be h(t)=-16t^2+20t+8 since 20 is the velocity, and once you input that onto a graph the answer of when it hits the ground is 1.569 seconds, so rounded is 1.6 seconds.

User Piyush Bansal
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4.7k points