1. A projectile is fired with initial speed 100 m/s at an angle 6° to the horizontal. Find the minimum altitude.
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The minimum height is the height at takeoff and landing of the projectile, so 0.
1. Which one or more of the following statements are correct?
a) The acceleration of the projectile remains constant during its upward flight.
b) The acceleration of the projectile remains constant during its downward flight.
c) The acceleration of the projectile increases during its downward flight.
d) The acceleration of the projectile decreases during its upward flight.
a) yes
b) yes
c) no
d) no
2.
How the initial speed affecting the range and the maximum height of the projectile.
\(1.\ Maximum\ height\ h_{max}\)
\(h=v\cdot t\cdot sin\ 6°-\frac{1}{2}\ gt^2\)
\(\frac{dh}{dt}=v\cdot \ sin\ 6°-g\cdot t=0\)
\(t=\frac{v\cdot sin\ 6°}{g}=\frac{100\cdot m\cdot sin\ 6°\cdot s^2}{s\cdot 9.81\cdot m}\)
\(t_{max}=1.0655\ s\)
\(h=v\cdot t\cdot sin\ 6°-\frac{1}{2}\ gt^2\)
\(h=(100m/s)\cdot (1.0655\ s)\cdot sin\ 6°-\frac{1}{2}\ (9,81m/s^2)(1.0655\ s)^2\)
\(h=11.138\ m-5.569\ m\)
\(h_{max}=5.569\ m\)
The maximum height of the projectile is 5.569 m.
\(2.\ Range\ R\)
\(t_R=2\cdot t_{max}=2\cdot 1.0655\ s\)
\(t_R=2.131\ s\)
\(R=v\cdot t_R\cdot cos\ 6°=100\frac{m}{s}\cdot 2.131\ s\cdot cos\ 6°\)
\(R=212\ m\)
The range of the projectile is 212 m.
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