Question

6. Two circus clowns, Art (A) and Bart (B), are shot from cannons towards each other. The plan is for them to grab hold of each other in the air and then do some tricks. Cannon A is aimed at angle ?? = 30° above the horizontal, and launches Art with an initial speed v? = 30 m/s. Cannon B is a distance L = 30 m away, and is aimed at an angle ?? = 60° above the horizontal. [Note: yes, these are unrealistically high speeds to shoot clowns out of a cannon. We'll talk about collisions later in the semester.] v? = 30 m/s ?? = 30° ?? = 60° L = 30 m (a) Find the launch speed required for Bart such that Art and Bart collide in midair. [Hint: consider the clowns' vertical motions.] (b) How far (horizontally) from Art's cannon will Art and Bart collide? How high above the ground will Art and Bart collide? (c) What is Art's velocity the instant before he collides with Bart? What is Bart's velocity the instant before he collides with Art? Each answer should be in the form v = v?i + v?j. (d) Sketch curves for Art's and Bart's position, velocity versus time. For example, the v? versus t graph should have a sketch of Art's horizontal velocity versus time, and a sketch of Bart's horizontal velocity versus time. Your sketches should be qualitatively correct, but need not be numerically accurate. Consider only the time interval between when they leave their cannons (t = 0) and when they collide.

          6. Two circus clowns, Art (A) and Bart (B), are shot from cannons towards each other. The plan is for them to grab hold of each other in the air and then do some tricks. Cannon A is aimed at angle ?? = 30° above the horizontal, and launches Art with an initial speed v? = 30 m/s. Cannon B is a distance L = 30 m away, and is aimed at an angle ?? = 60° above the horizontal. [Note: yes, these are unrealistically high speeds to shoot clowns out of a cannon. We'll talk about collisions later in the semester.]

v? = 30 m/s
?? = 30°
?? = 60°
L = 30 m

(a) Find the launch speed required for Bart such that Art and Bart collide in midair. [Hint: consider the clowns' vertical motions.]

(b) How far (horizontally) from Art's cannon will Art and Bart collide?
How high above the ground will Art and Bart collide?

(c) What is Art's velocity the instant before he collides with Bart?
What is Bart's velocity the instant before he collides with Art?
Each answer should be in the form v = v?i + v?j.

(d) Sketch curves for Art's and Bart's position, velocity versus time. For example, the v? versus t graph should have a sketch of Art's horizontal velocity versus time, and a sketch of Bart's horizontal velocity versus time. Your sketches should be qualitatively correct, but need not be numerically accurate. Consider only the time interval between when they leave their cannons (t = 0) and when they collide.

6. Two circus clowns, Art (A) and Bart (B), are shot from cannons towards each other. The plan is for them to grab hold of each other in the air and then do some tricks. Cannon A is aimed at angle ?? = 30° above the horizontal, and launches Art with an initial speed v? = 30 m/s. Cannon B is a distance L = 30 m away, and is aimed at an angle ?? = 60° above the horizontal. [Note: yes, these are unrealistically high speeds to shoot clowns out of a cannon. We'll talk about collisions later in the semester.]

v? = 30 m/s
?? = 30°
?? = 60°
L = 30 m

(a) Find the launch speed required for Bart such that Art and Bart collide in midair. [Hint: consider the clowns' vertical motions.]

(b) How far (horizontally) from Art's cannon will Art and Bart collide?
How high above the ground will Art and Bart collide?

(c) What is Art's velocity the instant before he collides with Bart?
What is Bart's velocity the instant before he collides with Art?
Each answer should be in the form v = v?i + v?j.

(d) Sketch curves for Art's and Bart's position, velocity versus time. For example, the v? versus t graph should have a sketch of Art's horizontal velocity versus time, and a sketch of Bart's horizontal velocity versus time. Your sketches should be qualitatively correct, but need not be numerically accurate. Consider only the time interval between when they leave their cannons (t = 0) and when they collide.

Added by Bryan W.

Question

Please give Ace some feedback