An object is fired into the air from a height of 250 meters and follows a path given by a vector valued function

Question

r(t) = <75t, 250+55t-4.9t^2>

The object is fired from a height of 250 meters, and follows a path given by the vector valued function above.

(1) Find the angle that the object was fired from, measured counter clockwise from the horizontal

36.2 degrees

(2) Find the maximum height above the ground the object reaches during its flight

404.3 m

(3) What is the speed of the object when it hits the ground?

116.4 m/s

(4) What is the total distance traveled by the object from when it was fired, to when it hit the ground?

I do not know if it means horizontal distance, or arc length. I've tried both, but nothing is working.

Answer 1

Total distance = arc length

We need to find when it hits the ground : h(t) = 0 , if you use quadratic formula => t=14.696

Then we find the arc length

integral from 0 to 14.696 of llr'(t)lldt = integral from 0 to 14.696 of root(75^2+(55-9.8t)^2)dt

=1273.9m