3. A ball rolls off of a table with a speed of 3.2 m/s. The table is 1.5 m high.a) When does the ball hit the ground? (Answer=0.55 s)b) How far away from the base of the table does the ball travel? (Answer=1.8 m)c) With what speed does the ball hit the floor? (Answer=6.3 m/s)
Question
- A ball rolls off of a table with a speed of 3.2 m/s. The table is 1.5 m high.a) When does the ball hit the ground? (Answer=0.55 s)b) How far away from the base of the table does the ball travel? (Answer=1.8 m)c) With what speed does the ball hit the floor? (Answer=6.3 m/s)
Solution
a) To find out when the ball hits the ground, we need to use the equation of motion that relates distance, initial velocity, time, and acceleration due to gravity. The equation is:
d = vt + 0.5at^2
where: d = distance (1.5 m) v = initial vertical velocity (0 m/s, because the ball is not thrown downwards or upwards, it just falls) a = acceleration due to gravity (9.8 m/s^2) t = time (which we are trying to find)
Substituting the known values into the equation, we get:
1.5 = 0t + 0.59.8*t^2
Solving for t, we get t = sqrt((2*1.5)/9.8) = 0.55 s
b) To find out how far away from the base of the table the ball travels, we need to use the equation for horizontal distance which is:
d = vt
where: d = horizontal distance v = initial horizontal velocity (3.2 m/s) t = time (0.55 s, which we found in part a)
Substituting the known values into the equation, we get:
d = 3.2*0.55 = 1.8 m
c) To find out with what speed the ball hits the floor, we need to use the Pythagorean theorem because the ball has both horizontal and vertical velocities. The equation is:
v = sqrt(vx^2 + vy^2)
where: v = final velocity vx = horizontal velocity (3.2 m/s) vy = vertical velocity (which can be found using the equation v = at, where a = 9.8 m/s^2 and t = 0.55 s)
Substituting the known values into the equation, we get:
vy = 9.8*0.55 = 5.39 m/s
Then, v = sqrt((3.2)^2 + (5.39)^2) = 6.3 m/s
Similar Questions
A small ball rolls horizontally off the edge of a tabletopthat is 1.20 m high. It strikes the floor at a point 1.52 m hori-zontally from the table edge. (a) How long is the ball in the air?(b) What is its speed at the instant it leaves the table?
4. A ball bearing rolls with constant velocity on a tabletop 0.950 m high. It rolls off and hits theground 0.35m from the edge of the table. How fast was the ball rolling?
1. A marble rolled off of a 1-m high tabletop with an initial horizontal velocity of 10 m/s.a) Determine its final velocity.b) How much time will it take for the marble to hit the floor?c) How far will the ball head forward before reaching the floor?2. A ball is hurled from a horizontal ground with a speed of 45 m/s at an angle of 35 0 from thehorizontal.a) What is the final horizontal velocity of the ball after 3.5 seconds?b) How much time will it take for it to reach its highest point?c) How much time will it take for it to reach the ground?d) What is the maximum height reached by the ball?e) What is the maximum horizontal distance covered by the ball?
A ball is rolled horizontally off a table with an initial speed of 0.21 m/s. A stopwatch measures the ball's trajectory time from table to the floor to be 0.3 s. What is the height of the table? (g = 9.8 m/s2 and air resistance is negligible)Select one:a.0.44 mb.0.45 mc.0.01 md.0.38 me.0.5 m
A baseball catcher puts on an exhibition by catching a 0.10-kg ball dropped from a helicopter at a height of 81 m. What is the speed of the ball just before it hits the catcher's glove 1 m above the ground? (g = 9.8 m/s2 and ignore air resistance)Select one:a.39.6 m/sb.1568 m/sc.40.09 m/sd.28 m/se.0.05 m/s
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.