Answer :
Answer:
Two possible smallest and largest angles are 11.78° and 78.22°.
Step-by-step explanation:
Minigolf ball will follow a trajectory to get into the hole.
Since range of a trajectory is calculated by the formula,
[tex]R=\frac{u^{2}sin2\theta}{g}[/tex]
Where u = initial speed of the ball
θ = angle between the hole and direction in which the ball has been projected
g = gravitational pull
Now we plug in the values in the formula,
[tex]2=\frac{7^{2}sin(2\theta)}{9.8}[/tex]
sin2θ = [tex]\frac{2\times 9.8}{49}[/tex]
2θ = [tex]sin^{-1}(0.4)[/tex]
2θ = 23.57° or 156.43°
θ = 11.78° or 78.22°
Hence two possible smallest and largest angles are 11.78° and 78.22°.
The TWO possible angles with the horizontal for the ball to get in the hole are 11.92° and 78.08°
Range of a projectile
The formula for calculating the range of a projectile is expressed as:
- [tex]R=\frac{u^2sin 2\theta}{g}[/tex]
where:
- u is the initial velocity
- g is the acceleration due to gravity
- [tex]\theta[/tex] is the angle
Substitute the given parameters into the formula as shown:
[tex]R=\frac{u^2sin 2\theta}{g}\\2=\frac{7^2sin 2\theta}{9.8}\\49 sin 2 \theta = 19.8\\ sin 2 \theta =\frac{19.8}{49}\\ sin 2 \theta =0.4041\\2 \theta=23.83^0\\[/tex]
Calculate the required angle:
[tex]2 \theta = 23.83^0\\\theta = \frac{23.83}{2}\\ \theta =11.92^0[/tex]
The second angle is expressed as:
[tex]\theta_2 = 90 - 11.92\\\theta_2=78.08^0[/tex]
Hence the TWO possible angles with the horizontal for the ball to get in the hole are 11.92° and 78.08°
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