2 Problem 3.23A man stands on the roof of a 150 m tall building and throws a rock with a velocity of 30 m/s at an angle of 330 above the horizontal. Ignore air resistance. Calculate:The maximum height above the roof reached by the rockThe magnitude of the velocity of the rock just before it strikes the groundThe horizontal distance from the base of the building to the point where the rock strikes the ground.
4 What do we know? The x- and y-components of the initial velocity Vx0=30*cos(330)=25.16 m/sVy0=30*sin(330)=16.33 m/sThe acceleration in the y-direction: ay=-g=-9.8The acceleration in the x-direction: ax=0The initial height of the rock, 150 m, = y0The initial horizontal position of the rock, 0
11 What do we know?arad =3 g or 10 gR= 7.0 mNeed to find T
12 Plugging and Chuggingarad =3 g or 10 gR= 7.0 mNeed to find T
13 Problem 3.37A “moving sidewalk” in an airport moves at 1 m/s and is 35.0 m long. If a women steps on one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does she require to reach the opposite side ifShe walks in the same direction as the sidewalk is moving?She walks against the motion of the sidewalk?
15 Must find relative velocity Call the slide walk as reference frame A, therefore the woman’s velocity in this frame vA is 1.5 m/sCall a stationary observer frame of reference, B and the slidewalk’s velocity in this frame is vB =1.0 m/sThe end points are fixed in reference B so I must adjust the woman’s velocity to reference B
16 Two different velocities If the woman and slide are in the same direction:Vp/B=Vp/A+VA/BVp/A= velocity of woman relative to slidewalk=1.5 m/sVA/B= velocity of slidewalk relative to frame B=1.0 m/sVp/B=1+1.5=2.5 m/s
17 Two different velocities cont’d If the woman and slide are in the opposite directions:Vp/B=Vp/A+VA/BVp/A= velocity of woman relative to slidewalk=-1.5 m/sVA/B= velocity of slidewalk relative to frame B=1.0 m/sVp/B=1-1.5=-0.5 m/s
18 Finally, In the same direction: vp/B=d/t where d=35 m and Vp/B=2.5 m/s t=35/2.5=14 sIn the opposite direction: vp/B=d/t where d=35 m and Vp/B=0.5 m/st=35/0.5=70 s
19 Problem 3.58A baseball thrown at an angle of 600 above the horizontal strikes a building 18 m away at a point 8 m above the point it is thrown. Ignore air resistance.Find the magnitude of the initial velocity of the baseball ( the velocity with which the baseball is thrown)Find the magnitude and direction of the velocity just before it strikes the building.