A spring cannon can shoot its projectile at a maximun of 30m/s. what is the maximum height that the projectile will reach? How long will it take to rech that height?
Hint: consider the object's velocity at its maximum height
+118625 A spring cannon can shoot its projectile at a maximun of 30m/s. what is the maximum height that the projectile will reach? How long will it take to rech that height?
Hint: consider the object's velocity at its maximum height
It will go the highest if it is shot straight up. (you better not be underneath when id comes back down though.)
Gavity is downwards acceleration - it is about 9.8m/s^2
\(\ddot y=-9.8\\ \dot y =-9.8t+c\\ \mbox{velocity at t=0 is 30 so c=30}\\ \dot y =-9.8t+30\\ y =-\frac{9.8t^2}{2}+30t+k\\ \mbox{Let the initrial displacement be 0 then k=0}\\ y =-\frac{9.8t^2}{2}+30t\\ \)
the height will be greatest at the turning point which is where velocity =0
\(\begin{align*}-9.8t+30&=0\\ 9.8t&=30\\ t&=\frac{30}{9.8}\\ t&=3.0612\;sec \end{align*}\)
\(y=-\frac{9.8t^2}{2}+30t\\ y=-4.9t^2+30t\\ y=-4.*3.0612^2+30*3.0612\\\)
-4*3.0612^2+30*3.0612 = 54.35221824
Max height approx 54.35 metres
+36923 Agree with Melody EXCEPT there is a small error in her last line calculation:
-4 *3.0612^2+30*3.0612 = 54.35221824 should be
-4.9 *3.0612^2+30*3.0612 = 54.35221824 resulting in max height of 45.92 m
