Question

4.5. During a snowball fight, your opponent distracts you by throwing a snowball at you with a high arc. She throws snowballs with a speed of 23.3 m/s and the first is thrown at 70.0 degrees. As you are watching the first snowball, she throws a second at a lower angle. (a) If both snowballs cover the same horizontal distance, at what angle (degrees) should the second be thrown? (b) If the second snow ball is going to hit you while your attention is still focused on the first snowball, how soon (s) after the first snowball is thrown must the second be thrown? In other words, what is the delay between the two throws that will have both arriving at the same time?

Answer 1

Answer:

(a) θ = 20°

(b) Time Delay = 2.84 s

Explanation:

(a)

This is the case of the projectile motion. In projectile motion, for the same launch speed, the range of a projectile is the same for the complimentary launch angles. Hence, the snowball will have the same range when launched at 70°, at an angle of:

$\theta = 90^{0} - 70^{0}$

θ = 20°

(b)

The time of flight of snowball can be found by the following formula:

$T = \frac{2\ u\ Sin \theta}{g}$

where,

T = Time of flight = ?

u = launch speed = 23.3 m/s

g = acceleration due to gravity = 9.81 m/s²

For θ = 70° :

$T_{70} = \frac{(2)(23.3\ m/s)Sin70^{0}}{9.81\ m/s^{2}}$

T₇₀ = 4.46 s

For θ = 20° :

$T_{20} = \frac{(2)(23.3\ m/s)Sin20^{0}}{9.81\ m/s^{2}}$

T₂₀ = 1.62 s

Therefore, the time delay can be calculated as follows:

$Time\ Delay = T_{70} - T_{20}\\Time\ Delay = 4.46\ s - 1.62\ s$

Time Delay = 2.84 s

Answer 2

A. The angle at which the second ball should be thrown is 20°

B. The delay time between the two throws is 2.83 s

 

A. Determination of the angle at which the second ball should be thrown

From the question given above, we were told that:

• The first ball is thrown at angle of 70°.

• Both balls covers the same range.

From the above data, the angle at which the second ball should be thrown will be = 90 – 70 = 20°

B. How to determine the delay time between the two throws

I. Determination of the time of flight at angle 70°

• Initial velocity (u) = 23.3 m/s

• Acceleration due to gravity (g) = 9.8 m/s²

• Angle (θ) = 70°

• Time of flight (T) =?

T = 2uSineθ / g

T = (2 × 23.3 × Sine 70) / 9.8

T = 4.45 s

II. Determination of the time flight at angle 20°

• Initial velocity (u) = 23.3 m/s

• Acceleration due to gravity (g) = 9.8 m/s²

• Angle (θ) = 20°

• Time of flight (T) =?

T = 2uSineθ / g

T = (2 × 23.3 × Sine 20) / 9.8

T = 1.62 s

III. Determination of the delay time

• Time of flight for 70° = 4.45 s

• Time of flight for 20° = 1.62 s

• Delay time =?

Delay time = 4.45 – 1.62

Delay time = 2.83 s

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