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Ymorist [56]
2 years ago
5

A stone is thrown vertically into the air at an initial velocity of 96 ft/s. On Mars, the height s (in feet) of the stone above

the ground after t seconds is s=69t-6t2and on Earth it is s=69t-16t2. How much higher will the stone travel on Mars than on Earth?
Physics
1 answer:
vladimir1956 [14]2 years ago
6 0

Answer:

240 ft

Explanation:

t = Time taken

u = Initial velocity = 96 ft/s

v = Final velocity

s = Displacement

a = Acceleration = 12 m/s² on Mars 32 ft/s² on Earth negative due to upward direction

Mars

s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -12\times t^2\\\Rightarrow s=96t-6t^2\ ft

Earth

s=ut+\frac{1}{2}at^2\\\Rightarrow s=96\times t+\frac{1}{2}\times -32\times t^2\\\Rightarrow s=96t-16t^2\ ft

Differentiating the first equation with respect to time we get

\frac{ds}{dt}=96-12t

Equating with zero

0=96-12t\\\Rightarrow t=\frac{96}{12}=8\ s

Differentiating the second equation with respect to time we get

\frac{ds}{dt}=96-32t

Equating with zero

0=96-32t\\\Rightarrow t=\frac{96}{32}=3\ s

Applying the time taken to the above equations, we get

s=96t-6t^2\ ft\\\Rightarrow s=96\times 8-6\times 8^2\\\Rightarrow s=384

s=96t-16t^2\\\Rightarrow s=96\times 3-16\times 3^2\\\Rightarrow s=144

Difference in height = 384-144 = 240 ft

The stone will travel 240 ft higher on Mars

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