Energy Produced by water and heatfrom the inner core of the earth of the earth
Static friction opposes the movement of car from the state of rest.
Dynamic or kinetic friction opposes the movement of the car when car is running at any speed.
Imagine a right triangle where the legs represent the horizontal and vertical lengths of the string and the hypotenuse represents the length of the string.
Let us assign some values:
x = horizontal length in feet
50 = vertical length in feet
L = length of the string in feet
Because we are modeling these quantities with a right triangle, we can use the Pythagorean theorem to relate them with the following equation:
L² = x² + 50²
We want to find an equation for the change of L over time, so first differentiate both sides with respect to time t then solve for dL/dt:
2L(dL/dt) = 2x(dx/dt)
dL/dt = (x/L)(dx/dt)
First let's solve for x at the moment in time described in the problem using the Pythagorean theorem:
L² = x² + 50²
Given values:
L = 100ft
Plug in and solve for x:
100² = x² + 50²
x = 86.6ft
Now let's find dL/dt. Given values:
x = 86.6ft, L = 100ft, dx/dt = 4ft/sec
Plug in and solve for dL/dt:
dL/dt = (86.6/100)(4)
dL/dt = 3.46ft/sec
Answer:
5 seconds
Explanation:
The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:
d² = x² + y²
d² = (-39 + 40t)² + (228 + 30t)²
d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²
d² = 53505 + 10560t + 2500t²
The cheetah can run a total distance of:
105 * 7 = 735
The time t at this distance is:
735² = 53505 + 10560t + 2500t²
540225 = 53505 + 10560t + 2500t²
0 = -486720 + 10560t + 2500t²
0 = -24336 + 528t + 125t²
t = 12, -16.224
t can't be negative, so t = 12.
Therefore, the cheetah can wait 5 seconds before it has to start running.
