**51. ssm As a prank, someone drops a water-filled balloon out of a window. The balloon is released from rest at a height of 10.0 m above the ears of a man who is the target. Then, because of a guilty con- science, the prankster shouts a warning after the balloon is released. The warning will do no good, however, if shouted after the balloon reaches a certain point, even if the man could react infinitely quickly. Assuming that the air temperature is 20 °C and ignoring the effect of air resistance on the balloon, determine how far above the man's ears this point is.

What is the displacement (mm) of the dots ? Displacement (mm) Y1 = Y2 =  Y3 = Y4 = Y5 = Y6=  Y 7 = Y 8 = Y9 = Y 10 = Y 11 = Y 12 = Y 13 = Y 14 =

The position of a particle changes linearly with time, i.e. as one power of t, as given by the following:h(t) = ( 6.2 t + 7.4 ) meters Find the speed of the particle, in meters per second.

In 2004 a massive 10-30m high tsunami was created in the eastern Indian Ocean by anearthquake in Sumatra resulting in the loss of hundreds of thousands of lives. The coast of Africa lies7000km to the west of Sumatra. Knowing that tsunami’s propagate at a speed v = √gH, how longdid it take for the tsunami to strike Africa?

A particles position along the X axis is described by the function x(t)= A t + B t^2, where t is in seconds, x is in meters, and the constants A and B are given. Randomized variables A=-4.2 m/s B=7.9 m/s^2 Enter an expression, in terms of A, B, and t, for the velocity of the particle as a function of time. At what time, in seconds, is the particles velocity zero? 

The position of a particle is →r(t)=(5t2ˆx+6ˆy−4.5tˆz)r→(t)=(5t2x^+6y^-4.5tz^)  m. Determine its velocity and acceleration as a function of time.→v(t)=v→(t)= (    ˆx+x^+  ˆy+y^+  ˆzz^) m/s                                   →a(t)=a→(t)= ( ˆx+x^+  ˆy+y^+  ˆzz^) m/s2                                    What are its velocity and acceleration at time t=0t=0?→v(t=0)=v→(t=0)=       m/s                   →a(t=0)=a→(t=0)=       m/s2