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If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height above the ground (in meters) after t seconds is given by H = 15t − 1.86t2. (a) Find the velocity (in m/s) of the rock after 1 second. 11.5404 Incorrect: Your answer is incorrect. seenKey 11.28 m/s (b) Find the velocity (in m/s) of the rock when t = a. m/s (c) When (in seconds) will the rock hit the surface? (Round your answer to one decimal place.) t = s (d) With what velocity (in m/s) will the rock hit the surface?

Sagot :

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(a) The velocity (in m/s) of the rock after 1 second is 11.28 m/s.

(b) The velocity of the rock after 2 seconds is 7.56 m/s.

(c) The time for the block to hit the surface is 4.03.

(d) The velocity of the block at the maximum height is 0.

Velocity of the rock

The velocity of the rock is determined as shown below;

Height of the rock after 1 second; H(t) = 15(1) - 1.86(1)² = 13.14 m

v² = u² - 2gh

where;

  • g is acceleration due to gravity in mars = 3.72 m/s²

v² = (15)² - 2(3.72)(13.14)

v² = 127.23

v = √127.23

v = 11.28 m/s

Velocity of the rock when t = 2 second

v = dh/dt

v = 15 - 3.72t

v(2) = 15 - 3.72(2)

v(2) = 7.56 m/s

Time for the rock to reach maximum height

dh/dt = 0

15 - 3.72t = 0

t = 4.03 s

Velocity of the rock when it hits the surface

v = u - gt

v = 15 - 3.72(4.03)

v = 0

Learn more about velocity at maximum height here: https://brainly.com/question/14638187

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