A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch?
+23247 The rocket starts from point (0,0) and hits the ground at (111,0).
The vertex of the parabola will occur halfway between these two points, at x = 55.5, y = 72.3
An equation of the parabola will be: y = a(x - 55.5)² + 72.3
To find the value of a, use the point (0,0): 0 = a(0 - 55.5)² + 72.3 --> 0 = a(3080.25) + 72.3
---> a = -.02354
Equation: y = -0.02354(x - 55.5)² + 72.3 ---> y = -0.02354x² + 2.6126x
Find the first derivative: y' = -0.04708x + 2.6126
At x = 0: y' = 2.6126 <--- this is the slope at x = 0;
the angle will be the invtan(2.6126), which is approx 69°
+23247 The rocket starts from point (0,0) and hits the ground at (111,0).
The vertex of the parabola will occur halfway between these two points, at x = 55.5, y = 72.3
An equation of the parabola will be: y = a(x - 55.5)² + 72.3
To find the value of a, use the point (0,0): 0 = a(0 - 55.5)² + 72.3 --> 0 = a(3080.25) + 72.3
---> a = -.02354
Equation: y = -0.02354(x - 55.5)² + 72.3 ---> y = -0.02354x² + 2.6126x
Find the first derivative: y' = -0.04708x + 2.6126
At x = 0: y' = 2.6126 <--- this is the slope at x = 0;
the angle will be the invtan(2.6126), which is approx 69°
