An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. 1) The rope will break if the tension in it exceeds N and our hero's mass is 86.5 kg.
Figure 1 a) If the angle is , find the tension iin the rope.
b) What is the smallest value the angle can have if the rope is not to break?
A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s a long its initial line of motion with an acceleration of 30.0 m/s/s. At this time, its engines fail and the rocket proceeds to move as a projectile. Find:
a) the maximum altitude reached by the rocket
b) its total time of flight
c) its horizontal range.
A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60 m high. At the bottom, it strikes a block of mass=7.00 kg which is at rest on a horizontal surface in the picture. If the collision is elastic, and friction can be ignored, determine (a)the speeds of the two blocks after the collision, and (b) how far back up the incline the smaller mass will go.
A weatherman carried an aneroid barometer from the groundfloor to his office atop a tower. On the ground level, the barometer read 30.150 in Hg absolute; topside it read 28.607 in hg absolute. Assume that the average atmospheric air density was 0.075lb/ft3, estimate the height of the building.
The rotating blade of a blender turns with constant angular acceleration 1.25 rad/s2
a) How much time does it take to reach an angular velocity of 34.0 rad/s, starting from
b) Through how many revolutions does the blade turn in this time interval?