. [P] In R2, we are throwing a ball att = 0 from the point (0, h) towards the positive r direction. Our initial speed will be 10 m/s and our initial velocity vector makes an angle of 0 with the r-axis. The only acceleration acting on the ball is due to gravity, which we can approximate as a(t) = (0, –10). Our goal is to make a formula which will tell us where the ball lands, as a function of h and 0. (a) What is the initial velocity of the ball? (b) Find a parametric function for the position of the ball at time t; leave h and 0 as unknown constants throughout. (c) Find the time T at which the ball hits the r-axis as a function of h and 0. (d) Find the r-coordinate where the ball hits the r-axis as a function of h and 0. (e) [S] [C] Calculate where the ball lands if launched from a height of 5.3 meters and with an angle of 37°.

Question
6. [P] In R?, we are throwing a ball at t = 0 from the point (0, h) towards the positive r direction. Our
initial speed will be 10 m/s and our initial velocity vector makes an angle of 0 with the r-axis. The
only acceleration acting on the ball is due to gravity, which we can approximate as a(t) = (0, – 10).
Our goal is to make a formula which will tell us where the ball lands, as a function of h and 0.
(a) What is the initial velocity of the ball?
(b) Find a parametric function for the position of the ball at time t; leave h and 0 as unknown
constants throughout.
(c) Find the time T at which the ball hits the r-axis as a function of h and 0.
(d) Find the r-coordinate where the ball hits the r-axis as a function of h and 0.
(e) [S] [C] Calculate where the ball lands if launched from a height of 5.3 meters and with an angle
of 37°.
Expand
Transcribed Image Text

6. [P] In R?, we are throwing a ball at t = 0 from the point (0, h) towards the positive r direction. Our initial speed will be 10 m/s and our initial velocity vector makes an angle of 0 with the r-axis. The only acceleration acting on the ball is due to gravity, which we can approximate as a(t) = (0, – 10). Our goal is to make a formula which will tell us where the ball lands, as a function of h and 0. (a) What is the initial velocity of the ball? (b) Find a parametric function for the position of the ball at time t; leave h and 0 as unknown constants throughout. (c) Find the time T at which the ball hits the r-axis as a function of h and 0. (d) Find the r-coordinate where the ball hits the r-axis as a function of h and 0. (e) [S] [C] Calculate where the ball lands if launched from a height of 5.3 meters and with an angle of 37°.

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