Question

1) Let’s redo our Class 3 (Monday, April 3) experiment with projectiles...on Mars!(a) It turns out that if we throw an object upward from the surface of Mars, itsheight at time t is roughly given by the functionh(t) = −1.86t2 + v0t + 2,meters, where v0 is the velocity (in m/s) with which the object was thrown, andwhere we’re assuming, as we did in class, that the object began at a height ofabout 2 meters (a little taller than most of us!).Suppose that we time the flight of our object and find out that it’s in the airfor 10 seconds. Use this information and the formula for h(t) to determine theinitial velocity v0.

Answer 1

We know that the object is in the air for 10 seconds, so we can substitute t = 10 into the formula for h(t) and solve for v0:

h(t) = -1.86t^2 + v0t + 2

h(10) = -1.86(10)^2 + v0(10) + 2

h(10) = -186 + 10v0 + 2

h(10) = 10v0 - 184

Since the object was thrown upward, we know that its height at the end of the 10 seconds is 2 meters (the initial height). So we have:

h(10) = 2

10v0 - 184 = 2

10v0 = 186

v0 = 18.6 m/s

Therefore, the initial velocity of the object was 18.6 m/s.

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