Horizontal Trajectory

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A horizontal trajectory problem is a two-part problem because when an object is thrown it covers a horizontal distance due to initial velocity, and also behaves as a free falling object due to gravity pulling the object down. The object therefore has two velocities, a downward and horizontal velocity. Visit the following link to view a graphic of this situation: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra11

 

The downward velocity of the object is not constant because of gravity; therefore time in the air and velocity before it hits the ground can be calculated as if it was a free falling problem.

 

In a horizontal trajectory problem, air friction is neglected therefore horizontal velocity is constant. This concept allows us to calculate the total range covered by the object thrown with the simple equation:

 R = v_xot

 

where R = range

            v_xo = initial velocity thrown

            t = time in the air

 

Procedures for a Horizontal trajectory problem

 

1)      Calculate time in the air: t =

2)      Calculate total range: R = v_ot

3)      Calculate downward velocity: v_y = at

4)      Calculate velocity before it hits the ground: v = sqrt(v_o²   +   v_y²)

 

 

Visit a horizontal launch online simulator to view a graphic and calculations of this situation:

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra11

Procedures

1)      Set an initial launch velocity and height.

2)      Select equations to calculate range and time.

 

Assessment

1)      Email complete solutions to the following problems to the instructor. Use the link above to compare solutions.

a)      A rock is thrown from the top of a cliff 50 m above ground with an initial velocity of 15 m/s. What is the time spent in the air and the range achieved? What was the final velocity before it hits the ground?

b)      At what velocity must an object be thrown to cover a range of 20 m and from a height of 10 m?

2)      Using the horizontal launch simulator link above, design 2 word problems each with different initial conditions. Through Email, trade problems with a classmate to solve. Submit all final solutions to the instructor.