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### Chapter 7

Projectile Motion

Projectile Motion

- The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.

- Because we ignore air resistance, the only force acting on thrown objects is gravity.

- The object that has been given an initial thrust, fired, or thrown into air.

- The path of a projectile as it travels through space.

In Projectile Motion

- The vertical & horizontal components act independently & can be solved independently

- The only force acting vertically is the force of gravity causing downward acceleration.

- There are no net forces acting horizontally; thus, the horizontal velocity is constant.

- Use your velocity formulas to solve for vertical & horizontal motion independently.

- Solve for time in air 1st
- Always use the vertical component to solve for the time in air.

- After solving for the time in air, solve for the range or horizontal distanced traveled

A rock has been thrown horizontally at 4.0 m/s from a tower 49 m high. Calculate: tair, dH, and vH & vV the instant before impact:

A plane flying horizontally at 250 m/s at an altitude of 4.9 km high drops a bomb. Calculate: tair, dH, and vV the instant before impact:

Drill: A ball rolls at 75 cm/s off the edge of a 49 cm table. Calculate: tair, maximum vV,

and dH:

A car traveling at 1500 cm/s goes off the edge of a 0.49 km high cliff. Calculate: tair, dH, and maximum vV:

A car accelerates at 5.0 m/s high cliff. Calculate: t2 for 250 m before going off the edge of a 0.49 km high cliff. Calculate: t & max v on the ground, & t, dH, and max vV in air:

Drill: A bullet exits a 0.50 m barrel horizontally at 500.0 m/s from a height of 2.0 m. Calculate: (a & t)in barrel, (t, max vV, & dH)in air:

A cannon ball is fired at 1000.0 m/s at 53 m/s from a height of 2.0 m. Calculate: (o from horizontal. Calculate: max height, tair ,vVat impact, dH:

Repeat the last problem with a cannon ball exiting the barrel at the same speed with angles of 40o, 45o, & 50o

Assumming all factors are the same for that cannon, Calculate its maximum range:

Drill: A ball is thrown at 25 m/s at 45 Calculate its maximum range:o from horizontal. Calculate:

tair, hmax, vVmax, dH:

A ball is thrown at 25 m/s at 53 Calculate its maximum range:o from horizontal. Calculate: vV, vH, tair, hmax, & dH

A 25 Mg car is accelerated from rest at 5.0 m/s Calculate its maximum range:2 up a 250 m ramp at 37o from horizontal. Calculate: t, & vf on the ramp, and dV, dH, t, and maximum vV in air:

A 1.0 Mg block slides from rest down a 250 m ramp ( Calculate its maximum range:m = 0.20) at 37o from horizontal that ends 490 m above the ground. Calculate: t, & vf on the ramp, and dH, t, and maximum vV in air:

Review Calculate its maximum range:

A sled coasts off a 0.49 km cliff at Calculate its maximum range:

18 km /hr.

Calculate: tair, max vV, & dH:

A catapult launches a 250 kg rock at 100.0 m/s at 37 Calculate its maximum range:o from horizontal. Calculate: tup, dV, tair, & dH :

Define each of the following Calculate its maximum range:

- Distance Displacement
- Speed Force
- Velocity Acceleration

Give Units for each of the following Calculate its maximum range:

- Distance Displacement
- Speed Acceleration
- Velocity Force

Projectile Calculate its maximum range: MotionProjectileTrajectory

A 25 Mg sled slides from rest down a 500.0 m slope ( Calculate its maximum range:m = 0.10) at 37o from horizontal that ends 2.45 km above the ground. Calculate: t, & vf on the slope, and dH, tair, and the maximum vV in air:

A 250 Mg sled accelerates at 3.0 m/s Calculate its maximum range:2 up a 250 m ramp (m = 0.25) at 53o from horizontal. Calculate: Fa, tramp, vf ramp, tair, dv, & dH

A 0.10 Mg cycle is accelerated with a force of 500.0 N for 10.0 s before hitting a 25 m ramp at 37o from horizontal. Draw the system and Calculate: vat bottom & top of ramp, and t, dv, & dH in the air

An airplane is flying horizontally due west at 360 km/hr at an altitude of 0.49 km & drops a 2000 lb bomb. Draw the system and Calculate: tair, maximum vV, & dH.

A 50.0 kg person skis ( an altitude of 0.49 km & drops a 2000 lb bomb. Draw the system and Calculate: m = 0.010) down a 3.0 km ski trail with an average slope of 30o. Draw the system and Calculate: a, t, maximum v on the trail

British Ships had cannons with muzzle velocities of 400 m/s while the cannons at Ft McHenry could fire at 500 m/s. The British could elevate to 45o while the Americans could elevate to 18o. Which cannons had the greater range.

Expanding gases produce about 10,000 N of force in a gun barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s2.

a barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s

b

A

B

- a = 37o
- = 53o
Y = 1.00 kN

C

X

Y

a barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s

b

FV of A

FV of B

+

FV of C

A

B

FH of A

FH of C

FH of B

C

FH of C

Wx +

FV of C

WY

a barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s

b

A

B

FV of A

FV of B

FH of C

FH of A

C

FH of B

FV of C

FH of C

FV of C

Wx +

FV of C

WY

A 200.0 kg rock is catapulted at 53 barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/so from horizontal at about 0.10 km/s. Draw the system and Calculate: t, dv, & dH in the air

A rock is thrown at 37 barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/so from horizontal at about 25 m/s. Draw the system and Calculate: t, dv, & dH in the air

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