Formula of range is given by
[tex]R = \frac{v_o^2 sin2\theta}{g}[/tex]
here given that
[tex]v_0=37.2m/s[/tex]
θ=14.1∘
[tex]g=9.80m/s^2[/tex]
now by above equation
[tex]R = \frac{37.2^2 sin2*14.1}{9.80}[/tex]
R = 66.7 m
so range will be 66.1 m
The range of a projectile is about 66.7 m
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Acceleration is rate of change of velocity.
[tex]\boxed {a = \frac{v - u}{t} }[/tex]
[tex]\boxed {d = \frac{v + u}{2}~t }[/tex]
where:
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
[tex]\texttt{ }[/tex]
Let's recall Range of Projectile formula as follows:
[tex]\boxed{ R = \frac{ v_o^2 \sin 2\theta}{g} }[/tex]
where:
R = range of projectile ( m )
v₀ = initial speed of projectile ( m/s )
θ = angle of projection
g = gravitational acceleration ( m/s² )
Let us now tackle the problem!
[tex]\texttt{ }[/tex]
Given:
initial speed of projectile = v₀ = 37.2 m/s
angle of projection = θ = 14.1°
gravitational acceleration = g = 9.80 m/s²
Asked:
the range of a projectile = R = ?
Solution:
[tex]R = \frac{ v_o^2 \sin 2\theta}{g}[/tex]
[tex]R = \frac{ 37.2^2 \sin 2 (14.1^o)}{9.80}[/tex]
[tex]\boxed {R = 66.7 \texttt{ m}}[/tex]
[tex]\texttt{ }[/tex]
The range of a projectile is about 66.7 m
[tex]\texttt{ }[/tex]
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Physics
Chapter: Kinematics
