Question #beffb

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Answer 1 · 2017-04-21T20:26:45

a) # t = 2 \ s#
b) # t = 0 \ s#
c) # v=0 \ ms^(-1)#

We have height (or displacement) at time #t#, where #h=0# is at ground level, and +ve is measured upwards, is given by:

# h(t) = -4.9t^2+9.8t #

Differentiating wrt #t# will give us the speed:

# doth(t) = -9.8t+9.8 #

a) When is the rocket travelling at 9.8 m/s down?

# doth(t) = -9.8 #
# :. -9.8t+9.8 = -9.8 #
# :. -9.8t = -19.6 #
# :. t = 2 \ s#

b) When is the rocket travelling at 9.8m/s up?

# doth(t) = 9.8 #
# :. -9.8t+9.8 = 9.8 #
# :. -9.8t = 0 #
# :. t = 0 \ s#

c) How fast is the rocket travelling after 1 second?

When #t=1#:

# doth(t) = -9.8+9.8 #
# " "= 0 \ ms^(-1)#