Aim: How can we solve problems dealing with horizontally fired objects? Do Now: An object falls freely for 75 m. How long does it take to reach the ground? How fast is it moving upon impact? d = v i t + ½at m = (0 m/s)t + ½(-9.8 m/s 2 )t 2 t = 3.9 s v f = v i + at v f = (0 m/s) + (9.8 m/s 2 )(3.9 s) v f = 38.3 m/s

Demo A bullet is shot out horizontally from a gun. At the same time and from the same height, a second bullet is dropped to the ground. Which hits the ground first?

They hit at the same time!

What goes on vertically has no impact as to what goes on horizontally What do you notice about the horizontal motion and the vertical motion?

Used for problems such as: Horizontally fired objects such as bullets, cars driving off of cliffs, etc. Horizontally fired objects such as bullets, cars driving off of cliffs, etc. Dropping an object while moving, such as a bomb or humanitarian package. Dropping an object while moving, such as a bomb or humanitarian package. The shape of the path is a parabola The shape of the path is a parabola

Car off Cliff

Separate Components Velocity, acceleration, and distance have both horizontal (x) component, and vertical (y) component Velocity, acceleration, and distance have both horizontal (x) component, and vertical (y) component

Horizontal Components Horizontal velocity is constant: Horizontal velocity is constant: There is no horizontal acceleration: There is no horizontal acceleration: Horizontal distance (also known as the range) is found using this equation: Horizontal distance (also known as the range) is found using this equation: a = 0 m/s 2

Vertical Components For the vertical motion, the object is in free fall: For the vertical motion, the object is in free fall: Vertical acceleration = gravity: Vertical acceleration = gravity: Vertical distance (also known as the height) is found using the distance equation: Vertical distance (also known as the height) is found using the distance equation: v i = 0 m/s a = g = -9.8 m/s 2 d = v i t + ½at 2

Time Vertical and Horizontal time are equal: Vertical and Horizontal time are equal:

Separate your information according to vertical and horizontal x y v i = 0 m/s a = -9.8 m/s 2 d =height d = range t = t

Example Thelma and Louise drive off a cliff 75 m high with a speed of 15 m/s. Thelma and Louise drive off a cliff 75 m high with a speed of 15 m/s. How long does it take to hit the ground? How long does it take to hit the ground? x y v i = 0 m/s a = -9.8 m/s 2 d = -75 m t = ?

Determine which column you have enough information so that you can solve the problem. The vertical column has enough. Do not mix and match vertical and horizontal information!!! d = v i t + ½at m = (0 m/s)t + ½(-9.8 m/s 2 )t = -4.9t = t s = t

 How far from the base of the cliff do they land? x y v i = 0 m/s a = -9.8 m/s 2 d = -75 m t = 3.9 s d = ? d = 58.5 m

 How fast are they traveling vertically on impact? x y v i = 0 m/s a = -9.8 m/s 2 d = -75 m t = 3.9 s v f = ? t = 3.9 s d = 58.5 m v f = v i + at v f = (0 m/s) + (-9.8 m/s 2 )(3.9 s) v f = m/s

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