If a rock is propelled upward from the surface of Mars at a velocity of 93 m/sec, it reaches a height
s = 93t – 1.86t^2 after t sec.
a. Find the rock’s velocity and acceleration at time t.

v'(t)=93-3.72t
a''(t)=-3.73

b. How long does it take the rock to reach its highest point?

v'(t)= 93-3.72t=0

t=25s
c. How high does the rock go?

f(x)= 93(25)-1.86(25)^2=1162.5m

I couldn't find the last two.

d. How long does it take the rock to reach 1/4 of its maximum height?
e. How long is the rock aloft?

1. 👍 0
2. 👎 0
3. 👁 211
1. a, b, and c look correct. For d, divide your answer from c by 4, plug it into the height equation, and solve for t. For e, it took 25 to reach the peak so it will take twice that long to reach 0 again (set s=0 and solve for t).

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Science

Heat and pressure deep beneath the Earths surface can change any rock into A) chemical rock B) gemstone C) metamorphic rock D) sedimentary rock

2. ### Calc

If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t − 1.86t^2. (a) Find the velocity of the rock after one second. (b) Find the velocity of the rock

3. ### Math

A rock is thrown upward with a velocity of 12 meters per sec from the top of a 25 meter high cliff and it misses on it's way back down. When will the rock be 3 meters from water

4. ### Math

For this problem, a person standing on the edge of a cliff throws a rock directly upward. it is observed that 2 secs later the rock is at its maximum height (in feet) and that 5 secs after that (meaning 7 seconds after being

1. ### science

Heat and pressure deep beneath Earth’s surface can change any rock into A. chemical rock. B. gemstone. C. metamorphic rock. D. sedimentary rock. pls help

2. ### Algebra

A rock is thrown upward with a velocity of 14 meters per second from the top of a 20 meter high cliff, and misses the cliff on the way back down. When will the rock be 12 meters from ground level

3. ### Calculus

If a rock is thrown upward on the planet Mars with a velocity of 19 m/s, its height (in meters) after t seconds is given by H = 19t − 1.86t^2. When will the rock hit the surface?

4. ### physics

Mars Rover When the Mars rover was deployed on the surface of Mars in July 1997, radio signals took about 12 min to travel from Earth to the rover.How far was Mars from Earth at that time?

1. ### Calculus

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by y = 10t - 1.86t^2 a) Find the average velocity over the given time in intervals: (i) [1,2] (ii) [1,1.5]

2. ### physics

Meteorites from Mars Several meteorites found in Antarctica are believed to have come from Mars, including the famous ALH84001 meteorite that some believe contains fossils of ancient life on Mars. Meteorites from Mars are thought

3. ### Calculus

The acceleration due to gravity near the surface of Mars is 3.72ms^-2 . A rock is thrown straight up from the surface with an initial velocity of 23ms^-2 . How high does it go?

4. ### physics

On Mars, the acceleration due to gravity is 3.71 m/s2. How far would a rock fall in 3 s if you dropped it on Mars?