The starship Enterprise and the Millennium Falcon are both stationary, docked in

Question

The starship Enterprise and the Millennium Falcon are both stationary, docked in space so that the crews can exchange cookies. They later depart at the same time with Han Solo directing the Millennium Flacon at a speed of 300 m/s at an angle 45 degrees to the initial direction of Captain Kirk in the Enterprise which moves off at 400 m/s. At the instant the two vessels separate Captain Kirk realizes he left his favorite tea-cozy on the Millennium Falcon and directs Lieutenant Sulu to alter course to intercept Han Solo. What acceleration must the Enterprise undergo for its path to intersect the path of the Millennium Falcon in 40 seconds?

Explanation / Answer

For Flacon :

Along X-direction :

Vfox = initial velocity of falcon in X-direction = 300 Cos45 = 212.13 m/s

t = 40 sec

Dfx = displacement of falcon in X-direction = Vfox t = 212.13 x 40 = 8485.2 m

Along Y-direction :

Vfoy = initial velocity of falcon in Y-direction = 300 Sin45 = 212.13 m/s

t = 40 sec

Dfy = displacement of falcon in X-direction = Vfoy t = 212.13 x 40 = 8485.2 m

For enterprise :

Along X-direction :

Veox = initial velocity of enterprise in X-direction = 400 m/s

ax = acceleration

t = 40 sec

Dex = displacement of enterprise in X-direction = Veox t + 0.5 ax t2

for enterprise and falcon to intersect

Dfx = Dex

8485.2 = Veox t + 0.5 ax t2

8485.2 =400 (40) + 0.5 ax (40)2

ax = - 9.4 m/s2

Along Y-direction :

Veoy = initial velocity of enterprise in Y-direction = 0 m/s

ay = acceleration

t = 40 sec

Dey = displacement of enterprise in Y-direction = Veoy t + 0.5 ay t2

for enterprise and falcon to intersect

Dfy = Dey

8485.2 = Veoy t + 0.5 ay t2

8485.2 = 0 (40) + 0.5 ay (40)2

ay = 10.61 m/s2

Net acceleration = a = sqrt (ax2 + ay2) = sqrt((-9.4)2 + (10.61)2) = 14.2 m/s2

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