1. Consider a projectile, say a frictionless teddy bear, which is thrown at an angle of theta� with an initial
velocity of v0.
� a) For a fi�xed angle, �and the maximum height of the teddy bear.
� b) Calculate the distance that the teddy bear travels before returning (gently, of course) to the
ground (which is assumed to be
at).
� c) Use these pieces of information to �nd the angle which produces the maximum of the sum of height and distance.
usage of function. in these question.
its bit of maths and physics. ms .sue. use of function
To solve these questions, we can use the equations of projectile motion. Here's how you can solve each part:
a) To find the maximum height of the teddy bear, you can use the equation:
H = (v0^2 * sin^2(theta)) / (2 * g)
where H is the maximum height, v0 is the initial velocity, theta is the launch angle, and g is the acceleration due to gravity (approximately 9.8 m/s^2). Plug in the values for v0 and theta to calculate the maximum height.
b) To calculate the distance traveled by the teddy bear before returning to the ground, you can use the equation:
D = (v0^2 * sin(2 * theta)) / g
where D is the distance traveled. Plug in the values for v0 and theta to calculate the distance.
c) To find the angle that produces the maximum sum of height and distance, you can create a function that represents the sum of height and distance:
f(theta) = (v0^2 * sin^2(theta)) / (2 * g) + (v0^2 * sin(2 * theta)) / g
Now you can use optimization methods (e.g., differentiation) to find the value of theta that maximizes this function. By finding the derivative of the function with respect to theta and setting it equal to zero, you can solve for the theta value that produces the maximum.
Remember to convert the input angles to radians before calculating the trigonometric functions. You can use the math module in Python to perform these calculations.