A bee was flying along a helical path so that its position vector at time t...

A bee was flying along a helical path so that its position vector at time t was r(t) = (5 cos t) i + (5 sin t) j + 2t k. At t = 4 sec it had a heart attack and died instantly. Where did it land (that is where did it hit the xy-plane in terms of its coordinates)? Assume distance is in feet and time is in seconds so g = 32 ft per second per second.

Expert Solution

When bee got dead it will fall freely under gravity. There will be only one acceleration of been that will be acceleration due to gravity I downward direction. There we will calculate the position and the velocity of bee at t=4 sec. Then we will calculate the time taken by bee to reach on the xy plane after it got heart attack by considering the motion of bee along z axis. Then we will calculate x coordinate of bee by analyzing the motion of bee in x direction for that duration and in the similar way we will calculate the y coordinate of bee where it will land.

genius_generous answered 2 years ago

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