Upwardly fired projectiles Objects fired at an upward

Upwardly fired projectiles Objects fired at an upward angle have a horizontal and a vertical component of motion that can be found using the trig functions of sine, cosine, and tangent. Sketch this: a football is kicked at 14. 5 m/s at an angle of 32 degrees with respect to the ground. The line that is 14. 5 m/s is the resultant. Because the angle is 32 degrees, the out component is greater than the up component.

Upwardly fired projectiles Gravity only affects the vertical component of motion. The horizontal component is considered unaffected by gravity or by air resistance (for simplicity). Why? Newton’s first law: a football in motion tends to remain in motion in a straight line and at a CONSTANT speed until the forces acting on it are unbalanced. Assuming no air resistance, the projectile impacts the ground VERTICALLY at the same speed it was fired at originally, but in the opposite direction. Let’s look at what happens to the velocity and acceleration vectors during an event like this.

Upwardly fired projectiles resultant Horizontal component – unchanged throughout the event Vertical component – decreases through first half, then increases during second half

What happens to the height as the angle increases? As the angle increases, the height increases, up to 90 degrees where it is ALL vertical. There is no horizontal component at 90 deg.

What happens to the range as the angle increases? Range increases up to 45 degrees and then decreases after that. 45 deg = exactly half vertical and half horizontal velocity. Up component = out component at 45 deg.

Simple Calculations What was the horizontal component of motion for a soccer ball kicked at a 25 deg angle with respect to the ground if it has a range of 34. 5 m in 4. 26 s? What was the vertical component of motion for this?

Hang time The greater the firing angle, the greater the hang time. Why? An arrow is shot at an upward angle so that it has a horizontal velocity of 35. 6 m/s and an upward velocity of 67. 8 m/s. What is the resultant velocity? How long is it in the air?

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