Horizontal+projectile+motion

=Horizontal projectile motion=



As with all cases where the object is subject to gravity the value for a will always be 10msmedia type="custom" key="827701".

Note that for all calculations, initial vertical velocity (umedia type="custom" key="827689") = 0 msmedia type="custom" key="827699". If a velocity is given for the object that velocity is entirely horizontal velocity (umedia type="custom" key="827705").

Finding time of flight.
E.g. 1. A ball rolls off a table at 7msmedia type="custom" key="827699". If the table is 1.2m high, how long will it take for the ball to hit the floor?


 * SOLUTION:** The horizontal velocity is immaterial. The three known variables are:

u = 0 msmedia type="custom" key="827699". a = 10 ms. x = 1.2 mmedia type="custom" key="827701"

math \\ \displaystyle \mathbf{x=ut+\frac{1}{2}at^2}\\ \displaystyle \mathbf {x=\frac{1}{2}at^2}\\ \displaystyle \therefore \mathbf{t=\sqrt{\frac{2x}{a}}}\\ \displaystyle \mathbf{t=\sqrt{\frac{2 \times 1.2}{10}}}\\ \mathbf {t=\sqrt{0.24}}\\ \mathbf {t=0.49 sec}

math

Finding horizontal range.
E.g. 2. A ball rolls off a table at 7msmedia type="custom" key="827699". If the table is 1.2m high, how far from the base of the table will the ball land?


 * SOLUTION:** Firstly, find the time of flight as shown. Then multiply by horizontal velocity.

math \\\mathbf{dist=vel \times time}\\ \mathbf{dist=7 \times 0.49}\\ \mathbf{dist=3.43m} math

Finding final vertical velocity.
E.g. 3. A ball rolls off a table at 7msmedia type="custom" key="827699". If the table is 1.2m high, what is the vertical velocity with which the ball hits the floor?


 * SOLUTION:** Make sure you don't use the horizontal velocity as the initial vertical velocity. The initial vertical velocity is zero.

u = 0 msmedia type="custom" key="827699". a = 10 ms. x = 1.2 mmedia type="custom" key="827701"

math \\\mathbf{v^2=u^2+2ax}\\ \mathbf{v^2=0^2+(2 \times 10 \times 1.2)}\\ \mathbf{v^2=24}\\ \mathbf{v=4.9ms^{-1}} math

Finding speed at which the ball hits the floor.
E.g. 4. A ball rolls off a table at 7msmedia type="custom" key="827699". If the table is 1.2m high, what is the vertical velocity with which the ball hits the floor?


 * SOLUTION:** This is a vector question and you need to add the final horizontal and vertical velocity vectors.

Final horizontal velocity is 7msmedia type="custom" key="827699" since horizontal velocity remains constant throughout flight.

Final vertical velocity is 4.9msmedia type="custom" key="827699" which we found previously.

Use Pythagoras Theorem to solve for the final vector.

math \\ \mathbf{c^2=a^2+b^2}\\ \mathbf{c^2=7^2+4.9^2}\\ \mathbf{c^2=49+24.01}\\ \mathbf{c^2=73.01}\\ \mathbf{c=8.54ms^{-1}}\\ \\ \displaystyle \bf \tan \theta =\frac{O}{A}\\ \displaystyle \bf \theta=\tan^{-1}\big(\frac{O}{A}\big)\\ \displaystyle \bf \theta=\tan^{-1}\big(\frac{4.9}{7.0}\big)\\ \displaystyle \bf \theta=\tan^{-1}(0.7)\\ \displaystyle \bf \theta=35^{\circ}\\ math