Question

During a baseball game, an outfielder is running in a straight line to catch a batted ball. The ball has been batted with initial speed 31 m/s at an angle of 65◦ with the horizontal. The outfielder is originally 40 m away from the batter along the same direction the ball is batted, and starts running the same moment the ball is batted. At what speed does he need to run to catch the ball as it lands?5

Answer 1

Here for the baseball , given.

u= initial velocity =31 m/s. At angle thita= 65 degree.

So the range of the baseball is R= u^(2)xSin(2.thita)/g.

On putting the value we get as R=31^(2)xSin(2x65)/g

So we get ,R =75.12 metres.

The fileder was originally at distance of 40m given. Then the ditance required to be moved by fielder be d= 75.12-40=35.12m

Now time of flight of baseball is T=2usin(2.thita)/g=2x31xSin(65)/g=5.73 seconds.

So the required speed of the fielder be

V = d/T=35.12/5.73=6.13 m/ s.

Hence required speed of fielder will be 6.13m/s. in order to catch the ball.