Am Amtrak high-speed train is traveling due east when it passes a cannon just as

Question

Am Amtrak high-speed train is traveling due east when it passes a cannon just as it is fired. The cannon is oriented along the direction of motion of the train and has a launch angle of 45 degrees. A passenger on the train notices that from her point of view the cannon ball seems to be traveling only in the vertical direction. She notices the cannon ball hits the ground 10 seconds after being fired. What can she determine about the train's speed?

(A) From her observations the train must be traveling at about 176 km/hr

(B) She does not have enough information to estimate the train's speed

(C) From her observations the train is traveling about 129 km/hr

(D) From her observations the train is traveling about 251 km/hr

Explanation / Answer

We can consider train to be moving = horizontal speed of cannon ball as she sees only vertical motion

So time taken by ball to reach heighest point = 10/2 = 5s

Now calculating its vertical speed (initial)

v = u + at

u = 9.8*5 = 49 m/s

Hence if actual initial velocity of cannon is v

vsin45 = u = 49

Now horizontal velocity of cannon ball = vcos45 = vsin45 = 49m/s

= 176km/h

So answer is A

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